Algebra: 6 Combinatorial and asymptotic methods of algebra, non-associative structures
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English Russian |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1995
|
| Schriftenreihe: | Encyclopaedia of mathematical sciences
57 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Buchcover |
| Beschreibung: | 287 S. graph. Darst. |
| ISBN: | 3540546995 0387546995 |
Internformat
MARC
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| 245 | 1 | 0 | |a Algebra |n 6 |p Combinatorial and asymptotic methods of algebra, non-associative structures |c A. I. Kostrikin ... (eds.) |
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Datensatz im Suchindex
| _version_ | 1804124839836909568 |
|---|---|
| adam_text | A.I. KOSTNKIN I. R. SHAFAREVICH (EDS.) ALGEBRA VI COMBINATORIAL AND
ASYMPTOTIC METHODS OF ALGEBRA. NON-ASSOCIATIVE STMCTURES SPRINGER I.
COMBINATORIAL AND ASYMPTOTIC METHODS IN ALGEBRA V. A. UFNAROVSKIJ
TRANSLATED FROM THE RUSSIAN BY R. M. DIMITRIC CONTENTS PREFACE TO THE
ENGLISH EDITION 5 INTRODUCTION 6 §1. BASIC OBJECTS AND CONSTRUCTIONS 8
1.1. INTRODUCTION 8 1.2. WAYS OF DEFINING INFINITE-DIMENSIONAL ALGEBRAS
10 1.3. COMBINATORIAL APPROACH 12 1.4. CONNECTIONS BETWEEN DIFFERENT
WAYS OF DEFINING BY GENERATORS AND RELATIONS 14 1.5. MODULES 16 1.6. THE
TENSOR PRODUCT 18 1.7. COALGEBRAS. HOPFAND ROOS ALGEBRAS 19 1.8.
ELEMENTS OF HOMOLOGICAL ALGEBRA 22 §2. NORMAL WORDS AND A GROEBNER BASIS
OF AN IDEAL OF A FREE ALGEBRA 27 2.1. INTRODUCTION 27 2.2. BASIC
NOTATION. DEGREE AND ORDER 27 2.3. NORMAL WORDS. DECOMPOSITION OF A FREE
ALGEBRA INTO AN IDEAL AND ITS NORMAL COMPLEMENT 28 2.4. GROEBNER BASIS.
COMPLETE SYSTEM OF RELATIONS 29 2.5. REDUCTION. COMPOSITION. THE
COMPOSITUM LEMMA 29 2.6. EXAMPLES 30 2.7. GROEBNER BASIS IN THE
COMMUTATIVE CASE 32 2.8. REGULAER WORDS. BASIS OF A FREE LIE ALGEBRA 34
2.9. A COMPOSITION LEMMA FOR LIE ALGEBRAS 37 2 V. A. UFNAROVSKIJ 2.10.
THE TRIANGLE LEMMA 39 2.11. APPLICATIONS AND EXAMPLES OF COMPLETE
SYSTEMS OF RELATIONS 39 2.12. COMMENTS 42 §3. GRADED ALGEBRAS. THE
GOLOD-SHAFAREVICH THEOREM. ANICK S RESOLUTION 42 3.1. INTRODUCTION 42
3.2. GRADED ALGEBRAS 43 3.3. THE METHOD OF GENERATING FUNCTIONS 44 3.4.
THE FREE PRODUCT. EXACT SEQUENCES 46 3.5. THE GOLOD-SHAFAREVICH THEOREM
47 3.6. OBSTRUCTIONS. THE N-CHAINS. THE GRAPH OF CHAINS 49 3.7.
CALCULATING THE HUBERT SERIES 51 3.8. ANICK S RESOLUTION 54 3.9.
CALCULATING THE POINCARE SERIES 59 3.10. ASSOCIATED LATTICES OF
SUBSPACES AND ALGEBRAS WITH ONE RELATION. ALGEBRAS WITH QUADRATIC
RELATIONS 63 3.11. COMMENTS 67 §4. GENERIC ALGEBRAS. DIOPHANTINE
EQUATIONS 67 4.1. INTRODUCTION 67 4.2. ORDER PROPERTIES FOR SERIES 68
4.3. ALGEBRAS OF GLOBAL DIMENSION TWO 70 4.4. CONDITIONS OF
FINITE-DIMENSIONALITY 73 4.5. PROPERTIES OF THE SET OF HUBERT SERIES 74
4.6. ACTION OF A FREE ALGEBRA. DIOPHANTINE EQUATIONS 76 4.7. COMMENTS 81
§5. GROWTH OF ALGEBRAS AND GRAPHS 82 5.1. INTRODUCTION 82 5.2. THE
GROWTH. GEL FAND-KIRILLOV DIMENSION. SUPERDIMENSION 83 5.3. THE
EXPONENTIAL GROWTH 86 5.4. THE GROWTH OF A SERIES 87 5.5. THE GROWTH OF
THE UNIVERSAL ENVELOPING ALGEBRA 88 5.6. THE GROWTH OF GRAPHS 89 5.7.
GRAPHS FOR NORMAL WORDS 90 5.8. TRANSFORMATIONS OF GRAPHS. FORMULAS FOR
NORMAL WORDS. CALCULATION OF THE HUBERT SERIES 92 5.9. AN ALGORITHM FOR
CALCULATING THE GROWTH OF AN ALGEBRA . . 94 5.10. REGULAER LANGUAGES.
AUTOMATON ALGEBRAS 95 5.11. COMMENTS 98 §6. COMBINATORIAL LEMMAS AND
THEIR APPLICATIONS TO QUESTIONS OF NILPOTENCY. THE GROWTH OF GROUPS 98
6.1. INTRODUCTION 98 6.2. THE AVOIDABLE WORDS 99 I. COMBINATORIAL AND
ASYMPTOTIC METHODS IN ALGEBRA 3 6.3. COMPARISON AND EQUIVALENCY OF
WORDS. PERIODIC AND REGULAER WORDS 101 6.4. THEOREM ON HEIGHT 104 6.5.
NILPOTENCY. SANDWICHES 106 6.6. NILPOTENCY AND GROWTH IN GROUPS 110 6.7.
COMMENTS 114 §7. THE ALGEBRAS OF POLYNOMIAL GROWTH. THE MONOMIAL
ALGEBRAS 115 7.1. INTRODUCTION 115 7.2. PL-ALGEBRAS. BASIC DEFINITIONS
AND FACTS 116 7.3. CALCULATION OF HUBERT SERIES AND SERIES OF
CODIMENSIONS IN VARIETIES OF ALGEBRAS 118 7.4. PL-ALGEBRAS.
REPRESENTABILITY. T-PRIMARY AND NON-MATRIX VARIETIES. THE EQUALITY
PROBLEM 122 7.5. VARIETIES OF SEMIGROUPS 125 7.6. THE AUTOMATON MONOMIAL
ALGEBRAS 127 7.7. FINITE GLOBAL DIMENSION. RADICAL AND PL-PROPERTIES OF
THE MONOMIAL ALGEBRAS 129 7.8. EXAMPLES OF GROWTH OF ALGEBRAS.
PROPERTIES OF THE GEL FAND-KIRILLOV DIMENSION 130 7.9. FINITE GROEBNER
BASIS AND STRICTLY ORDERED ALGEBRAS .... 133 7.10. LIE ALGEBRAS OF
POLYNOMIAL GROWTH 135 7.11. COMMENTS 136 §8. PROBLEMS OF RATIONALITY 137
8.1. INTRODUCTION 137 8.2. RATIONAL DEPENDENCE. FORMULATION OF THE
FUNDAMENTAL THEOREM 137 8.3. EXAMPLES OF NON-RATIONAL SERIES 139 8.4.
CONTIGUOUS SETS. QUADRATIC ALGEBRAS. RELATION WITH HOPF ALGEBRAS 141
8.5. DIFFERENTIAL ALGEBRAS 144 8.6. COMMENTS 148 §9. LOCAL RINGS.
CW-COMPLEXES 149 9.1. INTRODUCTION 149 9.2. REGULARITY. COMPLETE
INTERSECTION. RATIONALITY 149 9.3. KOSZUL COMPLEX 151 9.4. NILPOTENT
ALGEBRAS AND RINGS WITH THE CONDITION 2K 3 = 0 153 9.5. HOPF ALGEBRAS,
DIFFERENTIAL ALGEBRAS AND CW-COMPLEXES 155 §10. OTHER COMBINATORIAL
QUESTIONS 156 10.1. INTRODUCTION 156 10.2. HYPERBOLIC GROUPS 156 10.3.
QUANTUM GROUPS AND QUADRATIC ALGEBRAS 158 10.4. COMMENTS 161 4 V. A.
UFNAROVSKIJ §11. APPENDIX 161 11.1. COMPUTER ALGEBRA 161 11.2.
COMMUTATIVE GROEBNER BASIS 162 11.3. N-CYCLIC SYSTEMS OF EQUATIONS 163
11.4. COMMUTATIVE ALGEBRAS WITH THE QUADRATIC RELATIONS . . . 165 11.5.
KOSZUL ALGEBRAS AND VERONESE SUBALGEBRAS 166 11.6. LIE ALGEBRAS AND
RATIONALITY 167 11.7. GELFAND-KIRILLOV DIMENSION, GROWTH AND MONOMIAL
ALGEBRAS 168 11.8. THE BURNSIDE PROBLEM AND SEMIGROUPS 169 11.9. THE
GENERATINGFUNCTIONOLOGY 170 REFERENCES 182 ADDITIONAL REFERENCES 193
|
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| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:52:03Z |
| institution | BVB |
| isbn | 3540546995 0387546995 |
| language | English Russian |
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| physical | 287 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series | Encyclopaedia of mathematical sciences |
| series2 | Encyclopaedia of mathematical sciences |
| spelling | Algebra Algebra 6 Combinatorial and asymptotic methods of algebra, non-associative structures A. I. Kostrikin ... (eds.) Berlin [u.a.] Springer 1995 287 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopaedia of mathematical sciences 57 Encyclopaedia of mathematical sciences ... Kombinatorische Algebra (DE-588)4735525-6 gnd rswk-swf Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Nichtassoziative Algebra (DE-588)4297760-5 gnd rswk-swf Kombinatorische Algebra (DE-588)4735525-6 s Asymptotische Methode (DE-588)4287476-2 s Nichtassoziative Algebra (DE-588)4297760-5 s DE-604 Kostrikin, Aleksej I. Sonstige oth Paršin, Aleksej Nikolaevič 1942-2022 Sonstige (DE-588)172519012 oth (DE-604)BV002494676 6 Encyclopaedia of mathematical sciences 57 (DE-604)BV024126459 57 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006933436&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006933436&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Buchcover |
| spellingShingle | Algebra Encyclopaedia of mathematical sciences Kombinatorische Algebra (DE-588)4735525-6 gnd Asymptotische Methode (DE-588)4287476-2 gnd Nichtassoziative Algebra (DE-588)4297760-5 gnd |
| subject_GND | (DE-588)4735525-6 (DE-588)4287476-2 (DE-588)4297760-5 |
| title | Algebra |
| title_alt | Algebra |
| title_auth | Algebra |
| title_exact_search | Algebra |
| title_full | Algebra 6 Combinatorial and asymptotic methods of algebra, non-associative structures A. I. Kostrikin ... (eds.) |
| title_fullStr | Algebra 6 Combinatorial and asymptotic methods of algebra, non-associative structures A. I. Kostrikin ... (eds.) |
| title_full_unstemmed | Algebra 6 Combinatorial and asymptotic methods of algebra, non-associative structures A. I. Kostrikin ... (eds.) |
| title_short | Algebra |
| title_sort | algebra combinatorial and asymptotic methods of algebra non associative structures |
| topic | Kombinatorische Algebra (DE-588)4735525-6 gnd Asymptotische Methode (DE-588)4287476-2 gnd Nichtassoziative Algebra (DE-588)4297760-5 gnd |
| topic_facet | Kombinatorische Algebra Asymptotische Methode Nichtassoziative Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006933436&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006933436&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002494676 (DE-604)BV024126459 |
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