Computational aspects of polynomial identities:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Wellesley, Mass.
Peters
2005
|
| Series: | Research notes in mathematics
9 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 359-372) and index |
| Physical Description: | xxi, 378 p. 24 cm |
| ISBN: | 1568811632 |
Staff View
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV036083024 | ||
| 003 | DE-604 | ||
| 005 | 20100319 | ||
| 007 | t | ||
| 008 | 100317s2005 xxu |||| 00||| eng d | ||
| 010 | |a 2004053474 | ||
| 020 | |a 1568811632 |9 1-568-81-163-2 | ||
| 035 | |a (OCoLC)55990342 | ||
| 035 | |a (DE-599)BVBBV036083024 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-29T | ||
| 050 | 0 | |a QA251 | |
| 082 | 0 | |a 512/.4 |2 22 | |
| 100 | 1 | |a Kanel-Belov, Alexei |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Computational aspects of polynomial identities |c Alexei Kanel-Belov, Louis Halle Rowen |
| 264 | 1 | |a Wellesley, Mass. |b Peters |c 2005 | |
| 300 | |a xxi, 378 p. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Research notes in mathematics |v 9 | |
| 500 | |a Includes bibliographical references (p. 359-372) and index | ||
| 650 | 4 | |a Analyse combinatoire | |
| 650 | 4 | |a Anneaux de polynômes | |
| 650 | 4 | |a PI-algèbres | |
| 650 | 7 | |a Teoria dos anéis |2 larpcal | |
| 650 | 4 | |a PI-algebras | |
| 650 | 4 | |a Polynomial rings | |
| 650 | 4 | |a Combinatorial analysis | |
| 650 | 0 | 7 | |a PI-Algebra |0 (DE-588)4309236-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Polynomring |0 (DE-588)4175268-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kombinatorische Analysis |0 (DE-588)4164746-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a PI-Algebra |0 (DE-588)4309236-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Polynomring |0 (DE-588)4175268-5 |D s |
| 689 | 1 | 1 | |a Kombinatorische Analysis |0 (DE-588)4164746-4 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Rowen, Louis Halle |d 1949- |e Verfasser |0 (DE-588)138161909 |4 aut | |
| 830 | 0 | |a Research notes in mathematics |v 9 |w (DE-604)BV005530429 |9 9 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018974052&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018974052 | ||
Record in the Search Index
| _version_ | 1804141141657911296 |
|---|---|
| adam_text | Contents
Preface xi
Symbols Commonly Used in Text xvii
1 Basic Results 1
1.1 Definitions and Examples 1
1.2 Capelli Identities and Finite Dimensional Algebras 8
1.3 Graded Algebras and Grassman Algebras 11
1.4 Identities and Central Polynomials of Matrices 14
1.5 The Identity of Algebraicity 22
1.6 Review of Major Structure Theorems in Pi-Theory 24
1.7 Representable Algebras 28
1.8 ACC in Ring Theory 39
2 Affine Pl-algebras 41
2.1 Words Applied to Affine Algebras 43
2.2 Shirshov s Height Theorem 44
2.3 The Shirshov Program 52
2.4 The Trace Ring 52
2.5 The Razmyslov-Kemer-Braun Theorem 64
2.6 Shirshov s Lemma Revisited 69
3 T-Ideals and Relatively Free Algebras 79
3.1 Sets of Identities and T-Ideals 80
3.2 Relatively Free Algebras 81
3.3 Relatively Free Algebras Without 1, and Their T-Ideals . . 83
3.4 Recognizing T-Ideals 87
3.5 Specht s Problem Posed 88
3.6 Solution of Specht s Problem for Grassman Algebras .... 91
vii
viii Contents
4 Specht s Problem in the Affine Case 95
4.1 Kemer s PI-Representability Theorem 95
4.2 The Kemer Index 101
4.3 Subdirectly Irreducible Algebras 107
4.4 Kemer s Lemmas 110
4.5 Specht s Problem Completed in the AfRne Case 126
4.6 Appendix: Applying Kemer s Theory 128
4.7 Razmyslov-Zubrilin Traces Revisited 130
4.8 Pumping and rf-Identities 135
5 Representations of Sn and Their Applications 141
5.1 Passage to F[Sn] 141
5.2 Review of the Representation Theory of Sn 144
5.3 Sra-Actions on Tn(V) 152
5.4 Codimensions and Regev s Exponential Bound Theorem . . 154
5.5 Multilinearization 163
5.6 Appendix: Representation Theory in Characteristic p 0 . 166
6 Superidentities and Kemer s Main Theorem 169
6.1 Superidentities 169
6.2 Kemer s Pl-Superrepresentability Theorem 177
6.3 Consequences of Kemer s theory 191
7 Pl-Algebras in Characteristic p 201
7.1 Positive Results 201
7.2 The Extended Grassman Algebra 204
7.3 Non-Finitely Based T-Ideals in Characteristic 2 209
7.4 Non-Finitely Based T-Ideals in Odd Characteristic 214
8 Recent Structural Results 235
8.1 Left Noetherian Pi-algebras Are Finitely Presented 235
8.2 Identities of Group Algebras and Enveloping Algebras . . . 240
9 Poincare-Hilbert Series and Gelfand-Kirillov Dimension 245
9.1 The Hilbert Series of an Algebra 245
9.2 Gelfand-Kirillov Dimension 248
9.3 Upper Bounds for the Gelfand-Kirillov Dimension 259
9.4 Rationality of Certain Hilbert Series 260
9.5 The Multivariate Poincare-Hilbert Series 265
Contents ix
10 More Representation Theory 267
10.1 Cocharacters 267
10.2 GL(F)-Representation Theory 270
11 Unified Theory of Identities 279
11.1 Identities in Universal Algebra 279
11.2 Varieties 281
11.3 Examples of Varieties of Algebras and their Theories .... 284
12 Trace Identities 293
12.1 Trace Polynomials and Identities 293
12.2 Finite Generation of Trace T-Ideals 302
12.3 Trace Codimensions 305
13 Exercises 309
14 Lists of Theorems and Examples 343
14.1 Major Theorems 343
14.2 Major Examples and Counterexamples 352
15 Some Open Questions 355
Bibliography 359
Index 371
|
| any_adam_object | 1 |
| author | Kanel-Belov, Alexei Rowen, Louis Halle 1949- |
| author_GND | (DE-588)138161909 |
| author_facet | Kanel-Belov, Alexei Rowen, Louis Halle 1949- |
| author_role | aut aut |
| author_sort | Kanel-Belov, Alexei |
| author_variant | a k b akb l h r lh lhr |
| building | Verbundindex |
| bvnumber | BV036083024 |
| callnumber-first | Q - Science |
| callnumber-label | QA251 |
| callnumber-raw | QA251 |
| callnumber-search | QA251 |
| callnumber-sort | QA 3251 |
| callnumber-subject | QA - Mathematics |
| ctrlnum | (OCoLC)55990342 (DE-599)BVBBV036083024 |
| dewey-full | 512/.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.4 |
| dewey-search | 512/.4 |
| dewey-sort | 3512 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02008nam a2200541zcb4500</leader><controlfield tag="001">BV036083024</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20100319 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">100317s2005 xxu |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2004053474</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1568811632</subfield><subfield code="9">1-568-81-163-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)55990342</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV036083024</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-29T</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA251</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.4</subfield><subfield code="2">22</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kanel-Belov, Alexei</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Computational aspects of polynomial identities</subfield><subfield code="c">Alexei Kanel-Belov, Louis Halle Rowen</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Wellesley, Mass.</subfield><subfield code="b">Peters</subfield><subfield code="c">2005</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xxi, 378 p.</subfield><subfield code="c">24 cm</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Research notes in mathematics</subfield><subfield code="v">9</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (p. 359-372) and index</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analyse combinatoire</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Anneaux de polynômes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">PI-algèbres</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Teoria dos anéis</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">PI-algebras</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Polynomial rings</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Combinatorial analysis</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">PI-Algebra</subfield><subfield code="0">(DE-588)4309236-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Polynomring</subfield><subfield code="0">(DE-588)4175268-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kombinatorische Analysis</subfield><subfield code="0">(DE-588)4164746-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">PI-Algebra</subfield><subfield code="0">(DE-588)4309236-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Polynomring</subfield><subfield code="0">(DE-588)4175268-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Kombinatorische Analysis</subfield><subfield code="0">(DE-588)4164746-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Rowen, Louis Halle</subfield><subfield code="d">1949-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)138161909</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Research notes in mathematics</subfield><subfield code="v">9</subfield><subfield code="w">(DE-604)BV005530429</subfield><subfield code="9">9</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018974052&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-018974052</subfield></datafield></record></collection> |
| id | DE-604.BV036083024 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:11:09Z |
| institution | BVB |
| isbn | 1568811632 |
| language | English |
| lccn | 2004053474 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018974052 |
| oclc_num | 55990342 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | xxi, 378 p. 24 cm |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Peters |
| record_format | marc |
| series | Research notes in mathematics |
| series2 | Research notes in mathematics |
| spelling | Kanel-Belov, Alexei Verfasser aut Computational aspects of polynomial identities Alexei Kanel-Belov, Louis Halle Rowen Wellesley, Mass. Peters 2005 xxi, 378 p. 24 cm txt rdacontent n rdamedia nc rdacarrier Research notes in mathematics 9 Includes bibliographical references (p. 359-372) and index Analyse combinatoire Anneaux de polynômes PI-algèbres Teoria dos anéis larpcal PI-algebras Polynomial rings Combinatorial analysis PI-Algebra (DE-588)4309236-6 gnd rswk-swf Polynomring (DE-588)4175268-5 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf PI-Algebra (DE-588)4309236-6 s DE-604 Polynomring (DE-588)4175268-5 s Kombinatorische Analysis (DE-588)4164746-4 s Rowen, Louis Halle 1949- Verfasser (DE-588)138161909 aut Research notes in mathematics 9 (DE-604)BV005530429 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018974052&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kanel-Belov, Alexei Rowen, Louis Halle 1949- Computational aspects of polynomial identities Research notes in mathematics Analyse combinatoire Anneaux de polynômes PI-algèbres Teoria dos anéis larpcal PI-algebras Polynomial rings Combinatorial analysis PI-Algebra (DE-588)4309236-6 gnd Polynomring (DE-588)4175268-5 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
| subject_GND | (DE-588)4309236-6 (DE-588)4175268-5 (DE-588)4164746-4 |
| title | Computational aspects of polynomial identities |
| title_auth | Computational aspects of polynomial identities |
| title_exact_search | Computational aspects of polynomial identities |
| title_full | Computational aspects of polynomial identities Alexei Kanel-Belov, Louis Halle Rowen |
| title_fullStr | Computational aspects of polynomial identities Alexei Kanel-Belov, Louis Halle Rowen |
| title_full_unstemmed | Computational aspects of polynomial identities Alexei Kanel-Belov, Louis Halle Rowen |
| title_short | Computational aspects of polynomial identities |
| title_sort | computational aspects of polynomial identities |
| topic | Analyse combinatoire Anneaux de polynômes PI-algèbres Teoria dos anéis larpcal PI-algebras Polynomial rings Combinatorial analysis PI-Algebra (DE-588)4309236-6 gnd Polynomring (DE-588)4175268-5 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
| topic_facet | Analyse combinatoire Anneaux de polynômes PI-algèbres Teoria dos anéis PI-algebras Polynomial rings Combinatorial analysis PI-Algebra Polynomring Kombinatorische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018974052&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005530429 |
| work_keys_str_mv | AT kanelbelovalexei computationalaspectsofpolynomialidentities AT rowenlouishalle computationalaspectsofpolynomialidentities |