Polynomial identities and asymptotic methods:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2005]
|
| Series: | Mathematical surveys and monographs
Volume 122 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 352 Seiten Illustrationen, Diagramme |
| ISBN: | 0821838296 9780821838297 |
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MARC
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| 245 | 1 | 0 | |a Polynomial identities and asymptotic methods |c Antonio Giambruno, Mikhail Zaicev |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2005] | |
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Record in the Search Index
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| adam_text | MATHEMATICAL SURVEYS AND MONOGRAPHS VOLUME 122 POLYNOMIAL IDENTITIES AND
ASYMPTOTIC METHODS ANTONIO GIAMBRUNO MIKHAIL ZAICEV AMERICAN
MATHEMATICAL SOCIETY CONTENTS PREFACE IX CHAPTER 1. POLYNOMIAL
IDENTITIES AND PI-ALGEBRAS 1 1.1. BASIC DEFINITIONS AND EXAMPLES 1 1.2.
T-IDEALS AND VARIETIES OF ALGEBRAS 3 1.3. HOMOGENEOUS AND MULTILINEAR
POLYNOMIALS 5 1.4. STABLE IDENTITIES AND GENERIC ELEMENTS 10 1.5.
SPECIAL TYPES OF IDENTITIES 12 1.6. SYMMETRIC FUNCTIONS 15 1.7.
IDENTITIES OF MATRIX ALGEBRAS 16 1.8. A THEOREM OF LEWIN 20 1.9.
IDENTITIES OF BLOCK-TRIANGULAR MATRICES 24 1.10. CENTRAL POLYNOMIALS IN
MATRIX ALGEBRAS 26 1.11. STRUCTURE THEOREMS 29 1.12. SOME APPLICATIONS
OF THE STRUCTURE THEOREMS 35 1.13. THE GELFAND-KIRILLOV DIMENSION OF A
PI-ALGEBRA 36 CHAPTER 2. ^-REPRESENTATIONS 43 2.1. FINITE DIMENSIONAL
REPRESENTATIONS 43 2.2. .^-REPRESENTATIONS 46 2.3. INDUCING
^-REPRESENTATIONS 50 2.4. N -ACTIONS ON MULTILINEAR POLYNOMIALS 52
2.5. HOOKS AND SYMMETRIC AND ALTERNATING SETS OF VARIABLES 57 CHAPTER 3.
GROUP GRADINGS AND GROUP ACTIONS 61 3.1. GROUP-GRADED ALGEBRAS 61 3.2.
ABELIAN GRADINGS AND GROUP ACTIONS 63 3.3. G-ACTIONS, G-GRADINGS AND
FREE ALGEBRAS 65 3.4. WEDDERBURN DECOMPOSITIONS 69 3.5. FINITE
DIMENSIONAL SIMPLE SUPERALGEBRAS 74 3.6. INVOLUTIONS ON MATRIX ALGEBRAS
77 3.7. SUPERALGEBRAS AND GRASSMANN ENVELOPES 80 3.8. SUPERCOMMUTATIVE
ENVELOPES 83 CHAPTER 4. CODIMENSION AND COLENGTH GROWTH 87 4.1.
CODIMENSIONS AND COLENGTHS 87 4.2. AN EXPONENTIAL UPPER BOUND FOR THE
CODIMENSIONS 94 4.3. IDENTITIES OF GRADED ALGEBRAS 97 4.4.
ROBINSON-SCHENSTED CORRESPONDENCE 101 4.5. COCHARACTERS OF PI-ALGEBRAS
104 VI CONTENTS 4.6. CAPELLI POLYNOMIALS AND THE STRIP THEOREM 107 4.7.
AMITSUR POLYNOMIALS AND HOOKS 108 4.8. FINITELY GENERATED SUPERALGEBRAS
110 4.9. COLENGTH GROWTH: A POLYNOMIAL UPPER BOUND 115 CHAPTER 5. MATRIX
INVARIANTS AND CENTRAL POLYNOMIALS 119 5.1. 5 N -ACTION ON TENSOR SPACE
119 5.2. TRACE IDENTITIES 122 5.3. A PRIMER OF MATRIX INVARIANTS 124
5.4. THE DISCRIMINANT 125 5.5. INVARIANTS AND CENTRAL POLYNOMIALS 128
5.6. CONSTRUCTING 5FE-MAPS 131 5.7. COMPUTING CENTRAL POLYNOMIALS 132
5.8. COCHARACTERS AND TRACE COCHARACTERS 135 5.9. MULTIALTERNATING
POLYNOMIALS 137 5.10. ASYMPTOTICS FOR THE CODIMENSIONS OF K X K MATRICES
139 CHAPTER 6. THE PI-EXPONENT OF AN ALGEBRA 143 6.1. THE EXPONENTIAL
GROWTH OF THE CODIMENSIONS 143 6.2. A CANDIDATE FOR THE PI-EXPONENT 145
6.3. GRADED IDENTITIES AND GRASSMANN ENVELOPES 151 6.4. GLUING YOUNG
TABLEAUX 155 6.5. EXISTENCE OF THE EXPONENT 160 6.6. COMPUTING THE
EXPONENT OF SOME ALGEBRAS 161 CHAPTER 7. POLYNOMIAL GROWTH AND LOW
PI-EXPONENT 165 7.1. THE GRASSMANN ALGEBRA AND STANDARD POLYNOMIALS 165
7.2. VARIETIES OF POLYNOMIAL GROWTH 169 7.3. LOCALLY NOETHERIAN
VARIETIES 175 7.4. POLYNOMIAL GROWTH AND BOUNDED MULTIPLICITIES 179 7.5.
TYPES OF POLYNOMIAL GROWTH 185 7.6. VARIETIES OF EXPONENT TWO 189
CHAPTER 8. CLASSIFYING MINIMAL VARIETIES 193 8.1. MINIMAL SUPERALGEBRAS
193 8.2. SOME EXAMPLES 196 8.3. THE SUPERENVELOPE OF A MINIMAL
SUPERALGEBRA 199 8.4. PRODUCTS OF VERBALLY PRIME T-IDEALS 205 8.5.
CLASSIFYING MINIMAL VARIETIES OF EXPONENTIAL GROWTH 207 8.6. SOME
CONSEQUENCES 211 CHAPTER 9. COMPUTING THE EXPONENT OF A POLYNOMIAL 215
9.1. THE EXPONENT OF STANDARD AND CAPELLI POLYNOMIALS 215 9.2. AN UPPER
BOUND FOR THE EXPONENT OF A POLYNOMIAL 219 9.3. POWERS OF STANDARD
POLYNOMIALS 225 9.4. ESSENTIAL HOOKS AND REDUCED ALGEBRAS 238 9.5. THE
EXPONENT OF AMITSUR POLYNOMIALS 242 9.6. THE EXPONENT OF A LIE MONOMIAL
245 9.7. EVALUATING POLYNOMIALS 247 9.8. ASYMPTOTICS FOR THE STANDARD
AND THE CAPELLI IDENTITIES 251 CONTENTS VII CHAPTER 10. G-IDENTITIES AND
GI S N - ACTION 255 10.1. G-IDENTITIES, G-CODIMENSIONS AND GI 5 N
-ACTION 255 10.2. DECOMPOSABLE MONOMIALS 259 10.3. ESSENTIAL
G-IDENTITIES. AMITSUR S THEOREM ON ^-IDENTITIES 261 10.4.
REPRESENTATIONS OF WREATH PRODUCTS 264 10.5. GRADED IDENTITIES AND
POLYNOMIAL GROWTH 267 10.6. THE Z 2 I 5 N -ACTION 272 10.7. FINITE
DIMENSIONAL ALGEBRAS WITH /?-ACTION 274 10.8. THE Z2-EXPONENT OF A
FINITE DIMENSIONAL ALGEBRA 276 10.9. SIMPLE AND SEMISIMPLE (^-ALGEBRAS
280 CHAPTER 11. SUPERALGEBRAS, *-ALGEBRAS AND CODIMENSION GROWTH 283
11.1. NOTATION AND MORE 283 11.2. *-VARIETIES OF ALMOST POLYNOMIAL
GROWTH 285 11.3. SUPERVARIETIES OF ALMOST POLYNOMIAL GROWTH 289 11.4.
CAPELLI IDENTITIES ON SUPERALGEBRAS 292 11.5. SUPERALGEBRAS AND
POLYNOMIAL GROWTH 294 11.6. *-ALGEBRAS AND THE NAGATA-HIGMAN THEOREM 296
11.7. POLYNOMIAL GROWTH OF THE *-CODIMENSIONS 298 11.8. SUPERVARIETIES
OF EXPONENT 2 301 11.9. FURTHER PROPERTIES 304 CHAPTER 12. LIE ALGEBRAS
AND NON-ASSOCIATIVE ALGEBRAS 307 12.1. INTRODUCTION TO LIE ALGEBRAS 307
12.2. IDENTITIES OF LIE ALGEBRAS 309 12.3. CODIMENSION GROWTH OF LIE
ALGEBRAS 314 12.4. EXPONENTS OF LIE ALGEBRAS 323 12.5. OVEREXPONENTIAL
CODIMENSION GROWTH 327 12.6. LIE SUPERALGEBRAS, ALTERNATIVE AND JORDAN
ALGEBRAS 328 12.7. THE GENERAL NON-ASSOCIATIVE CASE 330 APPENDIX A. THE
GENERALIZED-SIX-SQUARE THEOREM 333 A.I. THE THEOREM 333 A.2. BASICS 334
A.3. REPRESENTATIONS OF INTEGERS 336 A.4. A CRUCIAL LEMMA 338 A.5. THE
PROOF OF THEOREM A.I.2 339 BIBLIOGRAPHY 341 INDEX 349
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:10:55Z |
| institution | BVB |
| isbn | 0821838296 9780821838297 |
| language | English |
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| physical | xiii, 352 Seiten Illustrationen, Diagramme |
| publishDate | 2005 |
| publishDateSearch | 2005 |
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| publisher | American Mathematical Society |
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| spelling | Giambruno, Antonio 1949- Verfasser (DE-588)141137622 aut Polynomial identities and asymptotic methods Antonio Giambruno, Mikhail Zaicev Providence, Rhode Island American Mathematical Society [2005] © 2005 xiii, 352 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 122 PI-algebras Rings (Algebra) PI-Algebra (DE-588)4309236-6 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf PI-Algebra (DE-588)4309236-6 s DE-604 Algebraische Zahlentheorie (DE-588)4001170-7 s Zaicev, Mikhail Verfasser aut Erscheint auch als Online-Ausgabe 978-1-4704-1349-1 Mathematical surveys and monographs Volume 122 (DE-604)BV000018014 122 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018965216&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Giambruno, Antonio 1949- Zaicev, Mikhail Polynomial identities and asymptotic methods Mathematical surveys and monographs PI-algebras Rings (Algebra) PI-Algebra (DE-588)4309236-6 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| subject_GND | (DE-588)4309236-6 (DE-588)4001170-7 |
| title | Polynomial identities and asymptotic methods |
| title_auth | Polynomial identities and asymptotic methods |
| title_exact_search | Polynomial identities and asymptotic methods |
| title_full | Polynomial identities and asymptotic methods Antonio Giambruno, Mikhail Zaicev |
| title_fullStr | Polynomial identities and asymptotic methods Antonio Giambruno, Mikhail Zaicev |
| title_full_unstemmed | Polynomial identities and asymptotic methods Antonio Giambruno, Mikhail Zaicev |
| title_short | Polynomial identities and asymptotic methods |
| title_sort | polynomial identities and asymptotic methods |
| topic | PI-algebras Rings (Algebra) PI-Algebra (DE-588)4309236-6 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| topic_facet | PI-algebras Rings (Algebra) PI-Algebra Algebraische Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018965216&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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