Free algebras and PI-algebras: graduate course in algebra
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Singapore [u.a.]
Springer
2000
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 255 - 266 |
| Beschreibung: | XII, 271 S. |
| ISBN: | 9814021482 |
Internformat
MARC
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| 245 | 1 | 0 | |a Free algebras and PI-algebras |b graduate course in algebra |c author Vesselin Drensky |
| 264 | 1 | |a Singapore [u.a.] |b Springer |c 2000 | |
| 300 | |a XII, 271 S. | ||
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| 500 | |a Literaturverz. S. 255 - 266 | ||
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Datensatz im Suchindex
| _version_ | 1804127572892581888 |
|---|---|
| adam_text | Table of Contents
Preface vii
Acknowledgments ix
Introduction 1
1. Commutative, Associative and Lie Algebras 5
1.1 Basic Properties of Algebras 5
1.2 Free Algebras 9
1.3 The Poincare Birkhoff Witt Theorem 11
2. Algebras with Polynomial Identities 17
2.1 Definitions and Examples of PI Algebras 17
2.2 Varieties and Relatively Free Algebras 22
2.3 The Theorem of Birkhoff 24
3. The Specht Problem 27
3.1 The Finite Basis Property 27
3.2 Lie Algebras in Characteristic 2 29
4. Numerical Invariants of T Ideals 37
4.1 Graded Vector Spaces 37
4.2 Homogeneous and Multilinear Polynomial Identities 39
4.3 Proper Polynomial Identities 42
5. Polynomial Identities of Concrete Algebras 49
5.1 Polynomial Identities of the Grassmann Algebra 50
5.2 Polynomial Identities of the Upper Triangular Matrices .... 52
6. Methods of Commutative Algebra 59
6.1 Rational Hilbert Series 59
6.2 Nonmatrix Polynomial Identities 63
6.3 Commutative and Noncommutative Invariant Theory 67
xii Table of Contents
7. Polynomial Identities of the Matrix Algebras 77
7.1 The Amitsur Levitzki Theorem 77
7.2 Generic Matrices 86
7.3 Central Polynomials 89
7.4 Various Identities of Matrices 102
8. Multilinear Polynomial Identities 107
8.1 The Codimension Theorem of Regev 107
8.2 Algebras with Polynomial Growth of Codimensions 114
8.3 The Nagata Higman Theorem 118
8.4 The Theory of Kemer 121
9. Finitely Generated PI Algebras 127
9.1 The Problems of Burnside and Kurosch 127
9.2 The Shirshov Theorem 129
9.3 Growth of Algebras and Gelfand Kirillov Dimension 138
9.4 Gelfand Kirillov Dimension of PI Algebras 142
10. Automorphisms of Free Algebras 151
10.1 Automorphisms of Groups and Algebras 151
10.2 The Polynomial Algebra in Two Variables 156
10.3 The Free Associative Algebra of Rank Two 166
10.4 Exponential Automorphisms 171
10.5 Automorphisms of Relatively Free Algebras 176
11. Free Lie Algebras and Their Automorphisms 179
11.1 Bases and Subalgebras of Free Lie Algebras 179
11.2 Automorphisms of Free Lie Algebras 182
11.3 Automorphisms of Relatively Free Lie Algebras 186
12. The Method of Representation Theory 193
12.1 Representations of Finite Groups 194
12.2 The Symmetric Group 201
12.3 Multilinear Polynomial Identities 208
12.4 The Action of the General Linear Group 217
12.5 Proper Polynomial Identities 231
12.6 Polynomial Identities of Matrices 239
Test 251
References 255
Subject Index 267
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:35:29Z |
| institution | BVB |
| isbn | 9814021482 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008771720 |
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| physical | XII, 271 S. |
| publishDate | 2000 |
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| spelling | Drenskij, Veselin S. 1950- Verfasser (DE-588)121509338 aut Free algebras and PI-algebras graduate course in algebra author Vesselin Drensky Singapore [u.a.] Springer 2000 XII, 271 S. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 255 - 266 PI-Algebra (DE-588)4309236-6 gnd rswk-swf Freie Algebra (DE-588)4155280-5 gnd rswk-swf Freie Algebra (DE-588)4155280-5 s DE-604 PI-Algebra (DE-588)4309236-6 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008771720&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Drenskij, Veselin S. 1950- Free algebras and PI-algebras graduate course in algebra PI-Algebra (DE-588)4309236-6 gnd Freie Algebra (DE-588)4155280-5 gnd |
| subject_GND | (DE-588)4309236-6 (DE-588)4155280-5 |
| title | Free algebras and PI-algebras graduate course in algebra |
| title_auth | Free algebras and PI-algebras graduate course in algebra |
| title_exact_search | Free algebras and PI-algebras graduate course in algebra |
| title_full | Free algebras and PI-algebras graduate course in algebra author Vesselin Drensky |
| title_fullStr | Free algebras and PI-algebras graduate course in algebra author Vesselin Drensky |
| title_full_unstemmed | Free algebras and PI-algebras graduate course in algebra author Vesselin Drensky |
| title_short | Free algebras and PI-algebras |
| title_sort | free algebras and pi algebras graduate course in algebra |
| title_sub | graduate course in algebra |
| topic | PI-Algebra (DE-588)4309236-6 gnd Freie Algebra (DE-588)4155280-5 gnd |
| topic_facet | PI-Algebra Freie Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008771720&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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