Representation theory and higher algebraic K-theory:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, FL
Chapman & Hall/CRC
2007
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| Series: | Monographs and textbooks in pure and applied mathematics
287 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXV, 442 S. graph. Darst. |
| ISBN: | 158488603X 9781584886037 |
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MARC
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| 020 | |a 158488603X |c alk. paper |9 1-58488-603-X | ||
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| 245 | 1 | 0 | |a Representation theory and higher algebraic K-theory |c Aderemi Kuku |
| 264 | 1 | |a Boca Raton, FL |b Chapman & Hall/CRC |c 2007 | |
| 300 | |a XXV, 442 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Monographs and textbooks in pure and applied mathematics |v 287 | |
| 650 | 7 | |a K-teoria algébrica |2 larpcal | |
| 650 | 4 | |a K-théorie | |
| 650 | 4 | |a Représentations de catégories | |
| 650 | 4 | |a Représentations de groupes | |
| 650 | 7 | |a Álgebra |2 larpcal | |
| 650 | 4 | |a K-theory | |
| 650 | 4 | |a Representations of categories | |
| 650 | 4 | |a Representations of groups | |
| 650 | 0 | 7 | |a Darstellungstheorie |0 (DE-588)4148816-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische K-Theorie |0 (DE-588)4141839-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraische K-Theorie |0 (DE-588)4141839-6 |D s |
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| _version_ | 1804136240209985536 |
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| adam_text | REPRESENTATION THEORY AND HIGHER ALGEBRAIC K-THEORY ADEREMI KUKU
INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS TRIESTE, ITALY CHAPMAN &
HALL/CRC TAYLOR & FRANCIS CROUP BOCA RATON LONDON NEW YORK CHAPMAN &
HALL/CRC IS AN IMPRINT OF THE TAYLOR & FRANCIS CROUP, AN INFORMA
BUSINESS CONTENTS INTRODUCTION XV NOTES ON NOTATIONS XXV I REVIEW OF
CLASSICAL ALGEBRAIC /F-THEORY AND REP- RESENTATION THEORY 1 1 CATEGORY
OF REPRESENTATIONS AND CONSTRUCTIONS OF GROTHENDIECK GROUPS AND RINGS 3
1.1 CATEGORY OF REPRESENTATIONS AND G-EQUIVARIANT CATEGORIES 3 1.2
GROTHENDIECK GROUP ASSOCIATED WITH A SEMI-GROUP 8 1.3 K O OF SYMMETRIC
MONOIDAL CATEGORIES 11 1.4 KQ OF EXACT CATEGORIES - DEFINITIONS AND
EXAMPLES 16 EXERCISES 21 2 SOME FUNDAMENTAL RESULTS ON KO OF EXACT AND
ABELIAN CATE- GORIES - WITH APPLICATIONS TO ORDERS AND GROUPRINGS 23 2.1
SOME FUNDAMENTAL RESULTS ON KQ OF EXACT AND ABELIAN CATE- GORIES 23
{2.1) A DEVISSAGE THEOREM AND EXAMPLE . . . 23 (2. 1) B RESOLUTION
THEOREM AND EXAMPLES *.. . . 24 (2.1) C KO AND LOCALIZATION IN ABELIAN
CATEGORIES PLUS EXAMPLES . . 25 2.2 SOME FINITENESS RESULTS ON KQ AND GO
OF ORDERS AND GROUPRINGS 28 2.3 CLASS GROUPS OF DEDEKIND DOMAINS,
ORDERS, AND GROUPRINGS PLUS SOME APPLICATIONS 29 (2.3)^ CLASS GROUPS OF
DEDEKIND DOMAINS 30 (2.3) B CLASS GROUPS OF ORDERS AND GROUPRINGS 31
(2.3) APPLICATIONS * WALL FINITENESS OBSTRUCTION 33 2.4 DECOMPOSITION OF
GO(RG) (G ABELIAN GROUP) AND EXTENSIONS TO SOME NON-ABELIAN GROUPS 34
(2.4)^ DECOMPOSITION OF G O (RG), G ABELIAN 34 (2.4) B CONNECTIONS TO
THE GROUP SSF 36 (2.4) C EXTENSIONS TO SOME NON-ABELIAN GROUPS
(DIHEDRAL AND QUATERNION GROUPS) 37 EXERCISES 40 3 KI, K2 OF ORDERS AND
GROUPRINGS 43 3.1 DEFINITIONS AND BASIC PROPERTIES 43 (3.1)^ KI OF A
RING 43 (3.1) B K OF LOCAL RINGS AND SKEW FIELDS 45 (3.1) C
MENNICKE SYMBOLS 46 (3.1) D STABILITY FOR K X 46 3.2 K , SK OF ORDERS
AND GROUPRINGS; WHITEHEAD TORSION . . . . 47 (3.2)^ KI,SKI OF ORDERS AND
GROUPRINGS 47 (3.2) B APPLICATIONS - WHITEHEAD TORSION AND S-COBORDISM
THEOREM 49 3.3 THE FUNCTOR K 2 50 (3.3) A K 2 OF RINGS AND FIELDS 50
(3.3) B K2 OF DIVISION ALGEBRAS AND MAXIMAL ORDERS 55 (3.3) C K2 AND
PSEUDO-ISOTROPY 57 EXERCISES . 57 4 SOME EXACT SEQUENCES; NEGATIVE
K-THEORY 61 4.1 MAYER - VIETORIS SEQUENCES 61 4.2 LOCALIZATION SEQUENCES
63 4.3 EXACT SEQUENCE ASSOCIATED TO AN IDEAL OF A RING . . . . . . . .
65 4.4 NEGATIVE K-THEOVY K_ N , N POSITIVE INTEGER 66 (4.4) A LF, NF
FUNCTORS AND THE FUNCTORS K_ N 66 (4.4) S MAYER - VIETORIS SEQUENCE 67
(4.4) C EXACT SEQUENCE ASSOCIATED TO AN IDEAL 69 (4.4)- LOCALIZATION
SEQUENCE 69 (4.4) E K- N {A) :=K 0 (S N A)^ 72 (4.4) F K- N (A), A AN
ADDITIVE CATEGORY 72 4.5 LOWER IF-THEORY OF GROUPRINGS OF VIRTUALLY
INFINITE CYCLIC GROUPS 74 (4.5)^ FARRELL - JONES ISOMORPHISM CONJECTURE
74 (4.5) B A PRELIMINARY RESULT 77 (4.5) C LOWER IF-THEORY FOR V = G X A
T :..... 77. (4.5) D LOWER TF-THEORY FOR V = G O * G X 78 SOME
APPLICATIONS 81 EXERCISES 82 II HIGHER ALGEBRAIC K-THEORY AND INTEGRAL
REPRE- SENTATIONS 85 5 HIGHER ALGEBRAIC K-THEORY * DEFINITIONS,
CONSTRUCTIONS, AND RELEVANT EXAMPLES 87 5.1 THE PLUS CONSTRUCTION AND
HIGHER/F-THEORY OF RINGS 87 (5.1) 71 THE PLUS CONSTRUCTION 87 5.2
CLASSIFYING SPACES AND HIGHER K-THEORY OF EXACT CATEGORIES -
CONSTRUCTIONS AND EXAMPLES 91 {B.2.) A SIMPLICIAL OBJECTS AND
CLASSIFYING SPACES 91 (5.2) B HIGHER IIT-THEORY OF EXACT CATEGORIES -
DEFINITIONS AND EXAM- PLES 93 (5.2) C IF-GROUPS AS HOMOTOPY GROUPS OF
SPECTRA 96 5.3 HIGHER FIT-THEORY OF SYMMETRIC MONOIDAL CATEGORIES -
DEFINITIONS AND EXAMPLES 98 5.4 HIGHER K -THEORY OF WALDHAUSEN
CATEGORIES - DEFINITIONS AND EXAMPLES 100 EXERCISES 104 ! SOME
FUNDAMENTAL RESULTS AND EXACT SEQUENCES IN HIGHER K- THEORY 107 6.1 SOME
FUNDAMENTAL THEOREMS 107 (6.1) A RESOLUTION THEOREM 107 (6.1) B
ADDITIVITY THEOREM (FOR EXACT AND WALDHAUSEN CATEGORIES) , 108 (6.1) C
DEVISSAGE 109 6.2 LOCALIZATION 110 (6.2)^ LOCALIZATION SEQUENCE PLUS
EXAMPLES 110 (6.2) B FUNDAMENTAL THEOREM FOR HIGHER X-THEORY 114 6.3
SOME EXACT SEQUENCES IN THE K-THEORY OF WALDHAUSEN CATE- GORIES 115 6.4
EXACT SEQUENCE ASSOCIATED TO AN IDEAL; EXCISION; AND MAYER, - VIETORIS
SEQUENCES 116 EXERCISES 118 R SOME RESULTS ON HIGHER K-THEORY OF ORDERS,
GROUPRINGS, AND MODULES OVER EL CATEGORIES 121 7.1 SOME FINITENESS
RESULTS ON K N , G N , SK N , SG N OF ORDERS AND GROUPINGS 121 (7.1) 4
HIGHER K-THEORY OF MAXIMAL ORDERS 122 (7.1) B K N ,G N ,SK N , SG N OF
ARBITRARY ORDERS 133 7.2 RANKS OF K N (A), G N (A) OF ORDERS AND
GROUPRINGS PLUS SOME CONSEQUENCES 147 (7.2) 4 RANKS OF K N AND G N OF
ORDERS A 147 (7.2) B K 2N (A), G 2N (A) ARE FINITE FOR ALL N 1 AND FOR
ALL I?-ORDERS A 151 7.3 DECOMPOSITION OF G N {RG) N 0, G FINITE
ABELIAN GROUP; EXTENSIONS TO SOME NON-ABELIAN GROUPS, E.G., QUATERNION
AND DIHEDRAL GROUPS 153 (7.3)^ LENSTRA FUNCTOR AND THE DECOMPOSITION 153
(7.3) B G N {RH), H DIHEDRAL GROUP OR NON-ABELIAN GROUP OF ORDER PQ 160
(7.3) C G N (RH), H THE GENERALIZED QUATERNION GROUP OF ORDER 4.2 . 163
(7.3) D G N (RH), (H A NILPOTENT GROUP) PLUS A CONJECTURE OF HAM-
BLETON, TAYLOR, AND WILLIAMS 168 7.4 HIGHER DIMENSIONAL CLASS GROUPS OF
ORDERS AND GROUPRINGS 172 (7.4) A GENERALITIES ON HIGHER CLASS GROUPS
172 (7.4) B TORSION IN ODD DIMENSIONAL HIGHER CLASS GROUPS 176 (7.4) C
TORSION IN EVEN-DIMENSIONAL HIGHER CLASS GROUPS G^2R(A) OF ORDERS 180
7.5 HIGHER K-THEORY OF GROUPRINGS OF VIRTUALLY INFINITE CYCLIC GROUPS.
188 (7.5) A SOME PRELIMINARY RESULTS 189 (7.5) B K-THEORY FOR THE FIRST
TYPE OF VIRTUALLY INFINITE CYCLIC GROUPS 192 (7.5) C NIL-GROUPS FOR THE
SECOND TYPE OF VIRTUALLY INFINITE CYCLIC GROUPS 198 7.6 HIGHER K-THEORY
OF MODULES OVER EF CATEGORIES 202 (7.6) 4 GENERALITIES ON MODULES OVER
EF CATEGORIES C 203 (7.6) B K N {RC),SK N {RC) 205 (7.6) C G N (RC),SG
N (RC) 207 (7.6) D CARTAN MAP K N {RC) -* G N {RC) 208 (7.6) B PAIRINGS
AND MODULE STRUCTURES 209 7.7 HIGHER K-THEORY OF V(A)Q; A MAXIMAL ORDERS
IN DIVISION ALGEBRAS; G FINITE GROUP 210 (7.7) A A TRANSFER MAP IN
HIGHER K-THEORY NON-COMMUTATIVE ANALOGUE OF A RESULT OF R.G. SWAN : 211
(7.7) B HIGHER K-THEORY OF V(A)C, A A MAXIMAL ORDER IN A P-ADIC DIVISION
ALGEBRA 215 (7.7) C HIGHER K-THEORY OF V(A)Q, A A MAXIMAL ORDER IN
DIVISION ALGEBRAS OVER NUMBER FIELDS 219 EXERCISES 221 8 MOD-M AND
PROFINITE HIGHER K-THEORY OF EXACT CATEGORIES, ORDERS, AND GROUPINGS 225
8.1 MOD-M K-THEORY OF EXACT CATEGORIES, RINGS, AND ORDERS . . . . 225
8.2 PROFINITE K-THEORY OF EXACT CATEGORIES, RINGS AND ORDERS 231 8.3
PROFINITE K-THEORY OF P-ADIC ORDERS AND SEMI-SIMPLE ALGEBRAS 238 8.4
CONTINUOUS K-THEORY OF P-ADIC ORDERS :.... 244 EXERCISES : . . 249 III
MACKEY FUNCTORS, EQUIVARIANT HIGHER ALGEBRAIC K-THEORY, AND EQUIVARIANT
HOMOLOGY THEORIES 251 9 MACKEY, GREEN, AND BURNSIDE FUNCTORS 253 9.1
MACKEY FUNCTORS 253 9.2 COHOMOLOGY OF MACKEY FUNCTORS 265 9.3 GREEN
FUNCTORS, MODULES, ALGEBRAS, AND INDUCTION THEOREMS . 272 9.4 BASED
CATEGORY AND THE BURNSIDE FUNCTOR 278 (9.4) A BURNSIDE RING OF A BASED
CATEGORY 278 (9.4) B UNIVERSALITY OF THE BURNSIDE FUNCTOR 281 (9.4) C
ARITHMETIC STRUCTURE OF L(B), B A BASED CATEGORY 285 (9.4) D ARITHMETIC
STRUCTURE OF FI(G), G A FINITE GROUP 289 9.5 INDUCTION THEOREMS FOR
MACKEY AND GREEN FUNCTORS 297 9.6 DEFECT BASIS OF MACKEY AND GREEN
FUNCTORS 302 9.7 DEFECT BASIS FOR K^-FUNCTORS 313 EXERCISES . 324 10
EQUIVARIANT HIGHER ALGEBRAIC K-THEORY TOGETHER WITH RELATIVE
GENERALIZATIONS * FOR FINITE GROUP ACTIONS . 325 10.1 EQUIVARIANT HIGHER
ALGEBRAIC K-THEORY 325 10.2 RELATIVE EQUIVARIANT HIGHER ALGEBRAIC
K-THEORY 328 10.3 INTERPRETATION IN TERMS OF GROUP-RINGS 330 10.4 SOME
APPLICATIONS 332 EXERCISES 335 11 EQUIVARIANT HIGHER K-THEORY FOR
PROFINITE GROUP ACTIONS 337 11.1 EQUIVARIANT HIGHER K-THEORY - (ABSOLUTE
AND RELATIVE) . . . 337 11.2 COHOMOLOGY OF MACKEY FUNCTORS (FOR
PROFINITE GROUPS) . . . . 341 EXERCISES 344 12 EQUIVARIANT HIGHER
K-THEORY FOR COMPACT LIE GROUP ACTIONS 347 12.1 MACKEY AND GREEN
FUNCTORS ON THE CATEGORY A(G) OF HOMOGE- NEOUS SPACES 347 (12.1) 4 THE
ABELIAN GROUP U(G,X), G A COMPACT LIE GROUP, X A G-SPACE; THE CATEGORY
A(G) 347 (12.1) B MACKEY AND GREEN FUNCTORS ON A(G) 349 12.2 AN
EQUIVARIANT HIGHER K-THEORY FOR G-ACTIONS 351 12.3 INDUCTION THEORY FOR
EQUIVARIANT HIGHER K-FUNCTORS 353 (12.3) A REMARKS ON POSSIBLE
GENERALIZATIONS 356 EXERCISE 357 13 EQUIVARIANT HIGHER K-THEORY FOR
WALDHAUSEN CATEGORIES 359 13.1 EQUIVARIANT WALDHAUSEN CATEGORIES 360
13.2 EQUIVARIANT HIGHER K-THEORY CONSTRUCTIONS FOR WALDHAUSEN CATEGORIES
361 (13.2) A ABSOLUTE AND RELATIVE EQUIVARIANT THEORY 361 (13.2) B
EQUIVARIANT ADDITIVITY THEOREM 365 (13. 2) C EQUIVARIANT WALDHAUSEN
FIBRATION SEQUENCE 366 13.3 APPLICATIONS TO COMPLICIAL BI-WALDHAUSEN
CATEGORIES 368 13.4 APPLICATIONS TO HIGHER K-THEORY OF GROUPRINGS 369
EXERCISE 371 14 EQUIVARIANT HOMOLOGY THEORIES AND HIGHER K-THEORY OF
GROUPRINGS 373 14.1 CLASSIFYING SPACE FOR FAMILIES AND EQUIVARIANT
HOMOLOGY THEORY 374 (14.1) A CLASSIFYING SPACES FOR FAMILIES AND
G-HOMOLOGY THEORY . . 374 14.2 ASSEMBLY MAPS AND ISOMORPHISM CONJECTURES
380 14.3 FARRELL - JONES CONJECTURE FOR ALGEBRAIC K-THEORY 384 14.4 BAUM
- CONNES CONJECTURE 388 (14.4) A GENERALITIES ON BAUM - CONNES
CONJECTURE ^389 14.5 DAVIS - LUCK ASSEMBLY MAP FOR BC CONJECTURE AND ITS
IDENTIFI- CATION WITH ANALYTIC ASSEMBLY MAP 396 EXERCISE 402 APPENDICES
403 A SOME COMPUTATIONS 403 B SOME OPEN PROBLEMS 419 REFERENCES 423
INDEX 437
|
| adam_txt |
REPRESENTATION THEORY AND HIGHER ALGEBRAIC K-THEORY ADEREMI KUKU
INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS TRIESTE, ITALY CHAPMAN &
HALL/CRC TAYLOR & FRANCIS CROUP BOCA RATON LONDON NEW YORK CHAPMAN &
HALL/CRC IS AN IMPRINT OF THE TAYLOR & FRANCIS CROUP, AN INFORMA
BUSINESS CONTENTS INTRODUCTION XV NOTES ON NOTATIONS XXV I REVIEW OF
CLASSICAL ALGEBRAIC /F-THEORY AND REP- RESENTATION THEORY 1 1 CATEGORY
OF REPRESENTATIONS AND CONSTRUCTIONS OF GROTHENDIECK GROUPS AND RINGS 3
1.1 CATEGORY OF REPRESENTATIONS AND G-EQUIVARIANT CATEGORIES 3 1.2
GROTHENDIECK GROUP ASSOCIATED WITH A SEMI-GROUP 8 1.3 K O OF SYMMETRIC
MONOIDAL CATEGORIES 11 1.4 KQ OF EXACT CATEGORIES - DEFINITIONS AND
EXAMPLES 16 EXERCISES 21 2 SOME FUNDAMENTAL RESULTS ON KO OF EXACT AND
ABELIAN CATE- GORIES - WITH APPLICATIONS TO ORDERS AND GROUPRINGS 23 2.1
SOME FUNDAMENTAL RESULTS ON KQ OF EXACT AND ABELIAN CATE- GORIES 23
{2.1) A DEVISSAGE THEOREM AND EXAMPLE . . . 23 (2. 1) B RESOLUTION
THEOREM AND EXAMPLES *. . . 24 (2.1) C KO AND LOCALIZATION IN ABELIAN
CATEGORIES PLUS EXAMPLES . . 25 2.2 SOME FINITENESS RESULTS ON KQ AND GO
OF ORDERS AND GROUPRINGS 28 2.3 CLASS GROUPS OF DEDEKIND DOMAINS,
ORDERS, AND GROUPRINGS PLUS SOME APPLICATIONS 29 (2.3)^ CLASS GROUPS OF
DEDEKIND DOMAINS 30 (2.3) B CLASS GROUPS OF ORDERS AND GROUPRINGS 31
(2.3) APPLICATIONS * WALL FINITENESS OBSTRUCTION 33 2.4 DECOMPOSITION OF
GO(RG) (G ABELIAN GROUP) AND EXTENSIONS TO SOME NON-ABELIAN GROUPS 34
(2.4)^ DECOMPOSITION OF G O (RG), G ABELIAN 34 (2.4) B CONNECTIONS TO
THE GROUP "SSF" 36 (2.4) C EXTENSIONS TO SOME NON-ABELIAN GROUPS
(DIHEDRAL AND QUATERNION GROUPS) 37 EXERCISES 40 3 KI, K2 OF ORDERS AND
GROUPRINGS 43 3.1 DEFINITIONS AND BASIC PROPERTIES 43 (3.1)^ KI OF A
RING 43 (3.1) B K\ OF LOCAL RINGS AND SKEW FIELDS " ' 45 (3.1) C
MENNICKE SYMBOLS 46 (3.1) D STABILITY FOR K X 46 3.2 K\, SK\ OF ORDERS
AND GROUPRINGS; WHITEHEAD TORSION . . . . 47 (3.2)^ KI,SKI OF ORDERS AND
GROUPRINGS 47 (3.2) B APPLICATIONS - WHITEHEAD TORSION AND S-COBORDISM
THEOREM 49 3.3 THE FUNCTOR K 2 50 (3.3) A K 2 OF RINGS AND FIELDS 50
(3.3) B K2 OF DIVISION ALGEBRAS AND MAXIMAL ORDERS 55 (3.3) C K2 AND
PSEUDO-ISOTROPY 57 EXERCISES . 57 4 SOME EXACT SEQUENCES; NEGATIVE
K-THEORY 61 4.1 MAYER - VIETORIS SEQUENCES 61 4.2 LOCALIZATION SEQUENCES
63 4.3 EXACT SEQUENCE ASSOCIATED TO AN IDEAL OF A RING . . . . . . . .
65 4.4 NEGATIVE K-THEOVY K_ N , N POSITIVE INTEGER 66 (4.4) A LF, NF
FUNCTORS AND THE FUNCTORS K_ N 66 (4.4) S MAYER - VIETORIS SEQUENCE 67
(4.4) C EXACT SEQUENCE ASSOCIATED TO AN IDEAL 69 (4.4)- LOCALIZATION
SEQUENCE 69 (4.4) E K- N {A) :=K 0 (S N A)^ 72 (4.4) F K- N (A), A AN
ADDITIVE CATEGORY 72 4.5 LOWER IF-THEORY OF GROUPRINGS OF VIRTUALLY
INFINITE CYCLIC GROUPS 74 (4.5)^ FARRELL - JONES ISOMORPHISM CONJECTURE
74 (4.5) B A PRELIMINARY RESULT 77 (4.5) C LOWER IF-THEORY FOR V = G X A
T ':. 77. (4.5) D LOWER TF-THEORY FOR V = G O * G X 78 SOME
APPLICATIONS 81 EXERCISES 82 II HIGHER ALGEBRAIC K-THEORY AND INTEGRAL
REPRE- SENTATIONS 85 5 HIGHER ALGEBRAIC K-THEORY * DEFINITIONS,
CONSTRUCTIONS, AND RELEVANT EXAMPLES 87 5.1 THE PLUS CONSTRUCTION AND
HIGHER/F-THEORY OF RINGS 87 (5.1) 71 THE PLUS CONSTRUCTION 87 5.2
CLASSIFYING SPACES AND HIGHER K-THEORY OF EXACT CATEGORIES -
CONSTRUCTIONS AND EXAMPLES 91 {B.2.) A SIMPLICIAL OBJECTS AND
CLASSIFYING SPACES 91 (5.2) B HIGHER IIT-THEORY OF EXACT CATEGORIES -
DEFINITIONS AND EXAM- PLES 93 (5.2) C IF-GROUPS AS HOMOTOPY GROUPS OF
SPECTRA 96 5.3 HIGHER FIT-THEORY OF SYMMETRIC MONOIDAL CATEGORIES -
DEFINITIONS AND EXAMPLES 98 5.4 HIGHER K -THEORY OF WALDHAUSEN
CATEGORIES - DEFINITIONS AND EXAMPLES 100 EXERCISES 104 ! SOME
FUNDAMENTAL RESULTS AND EXACT SEQUENCES IN HIGHER K- THEORY 107 6.1 SOME
FUNDAMENTAL THEOREMS 107 (6.1) A RESOLUTION THEOREM 107 (6.1) B
ADDITIVITY THEOREM (FOR EXACT AND WALDHAUSEN CATEGORIES) , 108 (6.1) C
DEVISSAGE 109 6.2 LOCALIZATION 110 (6.2)^ LOCALIZATION SEQUENCE PLUS
EXAMPLES 110 (6.2) B FUNDAMENTAL THEOREM FOR HIGHER X-THEORY 114 6.3
SOME EXACT SEQUENCES IN THE K-THEORY OF WALDHAUSEN CATE- GORIES 115 6.4
EXACT SEQUENCE ASSOCIATED TO AN IDEAL; EXCISION; AND MAYER, - VIETORIS
SEQUENCES 116 EXERCISES 118 R SOME RESULTS ON HIGHER K-THEORY OF ORDERS,
GROUPRINGS, AND MODULES OVER 'EL' CATEGORIES 121 7.1 SOME FINITENESS
RESULTS ON K N , G N , SK N , SG N OF ORDERS AND GROUPINGS 121 (7.1)" 4
HIGHER K-THEORY OF MAXIMAL ORDERS 122 (7.1) B K N ,G N ,SK N , SG N OF
ARBITRARY ORDERS 133 7.2 RANKS OF K N (A), G N (A) OF ORDERS AND
GROUPRINGS PLUS SOME CONSEQUENCES 147 (7.2) 4 RANKS OF K N AND G N OF
ORDERS A 147 (7.2) B K 2N (A), G 2N (A) ARE FINITE FOR ALL N 1 AND FOR
ALL I?-ORDERS A 151 7.3 DECOMPOSITION OF G N {RG) N 0, G FINITE
ABELIAN GROUP; EXTENSIONS TO SOME NON-ABELIAN GROUPS, E.G., QUATERNION
AND DIHEDRAL GROUPS 153 (7.3)^ LENSTRA FUNCTOR AND THE DECOMPOSITION 153
(7.3) B G N {RH), H DIHEDRAL GROUP OR NON-ABELIAN GROUP OF ORDER PQ 160
(7.3) C G N (RH), H THE GENERALIZED QUATERNION GROUP OF ORDER 4.2 . 163
(7.3) D G N (RH), (H A NILPOTENT GROUP) PLUS A CONJECTURE OF HAM-
BLETON, TAYLOR, AND WILLIAMS 168 7.4 HIGHER DIMENSIONAL CLASS GROUPS OF
ORDERS AND GROUPRINGS 172 (7.4) A GENERALITIES ON HIGHER CLASS GROUPS
172 (7.4) B TORSION IN ODD DIMENSIONAL HIGHER CLASS GROUPS 176 (7.4) C
TORSION IN EVEN-DIMENSIONAL HIGHER CLASS GROUPS G^2R(A) OF ORDERS 180
7.5 HIGHER K-THEORY OF GROUPRINGS OF VIRTUALLY INFINITE CYCLIC GROUPS.
188 (7.5) A SOME PRELIMINARY RESULTS 189 (7.5) B K-THEORY FOR THE FIRST
TYPE OF VIRTUALLY INFINITE CYCLIC GROUPS 192 (7.5) C NIL-GROUPS FOR THE
SECOND TYPE OF VIRTUALLY INFINITE CYCLIC GROUPS 198 7.6 HIGHER K-THEORY
OF MODULES OVER 'EF CATEGORIES 202 (7.6)" 4 GENERALITIES ON MODULES OVER
'EF CATEGORIES C 203 (7.6) B K N {RC),SK N {RC) 205 (7.6) C G N (RC),SG
N (RC) 207 (7.6) D CARTAN MAP K N {RC) -* G N {RC) 208 (7.6) B PAIRINGS
AND MODULE STRUCTURES 209 7.7 HIGHER K-THEORY OF V(A)Q; A MAXIMAL ORDERS
IN DIVISION ALGEBRAS; G FINITE GROUP 210 (7.7) A A TRANSFER MAP IN
HIGHER K-THEORY NON-COMMUTATIVE ANALOGUE OF A RESULT OF R.G. SWAN : 211
(7.7) B HIGHER K-THEORY OF V(A)C, A A MAXIMAL ORDER IN A P-ADIC DIVISION
ALGEBRA 215 (7.7) C HIGHER K-THEORY OF V(A)Q, A A MAXIMAL ORDER IN
DIVISION ALGEBRAS OVER NUMBER FIELDS 219 EXERCISES 221 8 MOD-M AND
PROFINITE HIGHER K-THEORY OF EXACT CATEGORIES, ORDERS, AND GROUPINGS 225
8.1 MOD-M K-THEORY OF EXACT CATEGORIES, RINGS, AND ORDERS . . . . 225
8.2 PROFINITE K-THEORY OF EXACT CATEGORIES, RINGS AND ORDERS 231 8.3
PROFINITE K-THEORY OF P-ADIC ORDERS AND SEMI-SIMPLE ALGEBRAS 238 8.4
CONTINUOUS K-THEORY OF P-ADIC ORDERS ':. 244 EXERCISES : . . 249 III
MACKEY FUNCTORS, EQUIVARIANT HIGHER ALGEBRAIC K-THEORY, AND EQUIVARIANT
HOMOLOGY THEORIES 251 9 MACKEY, GREEN, AND BURNSIDE FUNCTORS 253 9.1
MACKEY FUNCTORS 253 9.2 COHOMOLOGY OF MACKEY FUNCTORS 265 9.3 GREEN
FUNCTORS, MODULES, ALGEBRAS, AND INDUCTION THEOREMS . 272 9.4 BASED
CATEGORY AND THE BURNSIDE FUNCTOR 278 (9.4) A BURNSIDE RING OF A BASED
CATEGORY 278 (9.4) B UNIVERSALITY OF THE BURNSIDE FUNCTOR 281 (9.4) C
ARITHMETIC STRUCTURE OF L(B), B A BASED CATEGORY 285 (9.4) D ARITHMETIC
STRUCTURE OF FI(G), G A FINITE GROUP 289 9.5 INDUCTION THEOREMS FOR
MACKEY AND GREEN FUNCTORS 297 9.6 DEFECT BASIS OF MACKEY AND GREEN
FUNCTORS 302 9.7 DEFECT BASIS FOR K^-FUNCTORS 313 EXERCISES . 324 10
EQUIVARIANT HIGHER ALGEBRAIC K-THEORY TOGETHER WITH RELATIVE
GENERALIZATIONS * FOR FINITE GROUP ACTIONS . 325 10.1 EQUIVARIANT HIGHER
ALGEBRAIC K-THEORY 325 10.2 RELATIVE EQUIVARIANT HIGHER ALGEBRAIC
K-THEORY 328 10.3 INTERPRETATION IN TERMS OF GROUP-RINGS 330 10.4 SOME
APPLICATIONS 332 EXERCISES 335 11 EQUIVARIANT HIGHER K-THEORY FOR
PROFINITE GROUP ACTIONS 337 11.1 EQUIVARIANT HIGHER K-THEORY - (ABSOLUTE
AND RELATIVE) . . . 337 11.2 COHOMOLOGY OF MACKEY FUNCTORS (FOR
PROFINITE GROUPS) . . . . 341 EXERCISES 344 12 EQUIVARIANT HIGHER
K-THEORY FOR COMPACT LIE GROUP ACTIONS 347 12.1 MACKEY AND GREEN
FUNCTORS ON THE CATEGORY A(G) OF HOMOGE- NEOUS SPACES 347 (12.1)" 4 THE
ABELIAN GROUP U(G,X), G A COMPACT LIE GROUP, X A G-SPACE; THE CATEGORY
A(G) 347 (12.1) B MACKEY AND GREEN FUNCTORS ON A(G) 349 12.2 AN
EQUIVARIANT HIGHER K-THEORY FOR G-ACTIONS 351 12.3 INDUCTION THEORY FOR
EQUIVARIANT HIGHER K-FUNCTORS 353 (12.3) A REMARKS ON POSSIBLE
GENERALIZATIONS 356 EXERCISE 357 13 EQUIVARIANT HIGHER K-THEORY FOR
WALDHAUSEN CATEGORIES 359 13.1 EQUIVARIANT WALDHAUSEN CATEGORIES 360
13.2 EQUIVARIANT HIGHER K-THEORY CONSTRUCTIONS FOR WALDHAUSEN CATEGORIES
361 (13.2) A ABSOLUTE AND RELATIVE EQUIVARIANT THEORY 361 (13.2) B
EQUIVARIANT ADDITIVITY THEOREM 365 (13. 2) C EQUIVARIANT WALDHAUSEN
FIBRATION SEQUENCE 366 13.3 APPLICATIONS TO COMPLICIAL BI-WALDHAUSEN
CATEGORIES 368 13.4 APPLICATIONS TO HIGHER K-THEORY OF GROUPRINGS 369
EXERCISE 371 14 EQUIVARIANT HOMOLOGY THEORIES AND HIGHER K-THEORY OF
GROUPRINGS 373 14.1 CLASSIFYING SPACE FOR FAMILIES AND EQUIVARIANT
HOMOLOGY THEORY 374 (14.1) A CLASSIFYING SPACES FOR FAMILIES AND
G-HOMOLOGY THEORY . . 374 14.2 ASSEMBLY MAPS AND ISOMORPHISM CONJECTURES
380 14.3 FARRELL - JONES CONJECTURE FOR ALGEBRAIC K-THEORY 384 14.4 BAUM
- CONNES CONJECTURE 388 (14.4) A GENERALITIES ON BAUM - CONNES
CONJECTURE ^389 14.5 DAVIS - LUCK ASSEMBLY MAP FOR BC CONJECTURE AND ITS
IDENTIFI- CATION WITH ANALYTIC ASSEMBLY MAP 396 EXERCISE 402 APPENDICES
403 A SOME COMPUTATIONS 403 B SOME OPEN PROBLEMS 419 REFERENCES 423
INDEX 437 |
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| classification_rvk | SK 230 |
| ctrlnum | (OCoLC)71348752 (DE-599)BVBBV022246139 |
| dewey-full | 512/.66 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.66 |
| dewey-search | 512/.66 |
| dewey-sort | 3512 266 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV022246139 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:37:43Z |
| indexdate | 2024-07-09T20:53:15Z |
| institution | BVB |
| isbn | 158488603X 9781584886037 |
| language | English |
| lccn | 2006049287 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015456999 |
| oclc_num | 71348752 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XXV, 442 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Monographs and textbooks in pure and applied mathematics |
| series2 | Monographs and textbooks in pure and applied mathematics |
| spelling | Kuku, Aderemi O. Verfasser aut Representation theory and higher algebraic K-theory Aderemi Kuku Boca Raton, FL Chapman & Hall/CRC 2007 XXV, 442 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs and textbooks in pure and applied mathematics 287 K-teoria algébrica larpcal K-théorie Représentations de catégories Représentations de groupes Álgebra larpcal K-theory Representations of categories Representations of groups Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Algebraische K-Theorie (DE-588)4141839-6 gnd rswk-swf Algebraische K-Theorie (DE-588)4141839-6 s Darstellungstheorie (DE-588)4148816-7 s DE-604 Monographs and textbooks in pure and applied mathematics 287 (DE-604)BV000001885 287 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015456999&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kuku, Aderemi O. Representation theory and higher algebraic K-theory Monographs and textbooks in pure and applied mathematics K-teoria algébrica larpcal K-théorie Représentations de catégories Représentations de groupes Álgebra larpcal K-theory Representations of categories Representations of groups Darstellungstheorie (DE-588)4148816-7 gnd Algebraische K-Theorie (DE-588)4141839-6 gnd |
| subject_GND | (DE-588)4148816-7 (DE-588)4141839-6 |
| title | Representation theory and higher algebraic K-theory |
| title_auth | Representation theory and higher algebraic K-theory |
| title_exact_search | Representation theory and higher algebraic K-theory |
| title_exact_search_txtP | Representation theory and higher algebraic K-theory |
| title_full | Representation theory and higher algebraic K-theory Aderemi Kuku |
| title_fullStr | Representation theory and higher algebraic K-theory Aderemi Kuku |
| title_full_unstemmed | Representation theory and higher algebraic K-theory Aderemi Kuku |
| title_short | Representation theory and higher algebraic K-theory |
| title_sort | representation theory and higher algebraic k theory |
| topic | K-teoria algébrica larpcal K-théorie Représentations de catégories Représentations de groupes Álgebra larpcal K-theory Representations of categories Representations of groups Darstellungstheorie (DE-588)4148816-7 gnd Algebraische K-Theorie (DE-588)4141839-6 gnd |
| topic_facet | K-teoria algébrica K-théorie Représentations de catégories Représentations de groupes Álgebra K-theory Representations of categories Representations of groups Darstellungstheorie Algebraische K-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015456999&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
| work_keys_str_mv | AT kukuaderemio representationtheoryandhigheralgebraicktheory |