Verfügbarkeit: Frobenius Algebras | Technische Universität München

Frobenius Algebras: 1 Basic representation theory

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Bibliographische Detailangaben
Beteiligte Personen:	Skowroński, Andrzej 1950-2020 (VerfasserIn), Yamagata, Kunio (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Zürich European Mathematical Society 2011
Schlagwörter:	Hopf-Algebra Hecke-Algebra Frobenius-Algebra
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027451058&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XI, 650 Seiten
ISBN:	9783037191026

Internformat

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Datensatz im Suchindex

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adam_text	Titel: Bd. 1. Frobenius algebras. Basic representation theory Autor: Skowroński, Andrzej Jahr: 2011 Contents Introduction ix I Algebras and modules 1 1 Algebras. 1 2 Representations of algebras and modules . 12 3 The Jacobson radical. 30 4 The Krull-Schmidt theorem. 41 5 Semisimple modules. 45 6 Semisimple algebras. 56 7 The Jordan-Holder theorem. 67 8 Projective and injective modules. 73 9 Hereditary algebras. 93 10 Nakayama algebras. 100 11 The Grothendieck group and the Cartan matrix. 105 12 Exercises. 109 II Monta theory 123 1 Categories and functors. 123 2 Bimodules. 125 3 Tensor products of modules . 133 4 Adjunctions and natural isomorphisms. 140 5 Progenerators. 151 6 Morita equivalence. 157 7 Morita-Azumaya duality. 175 8 Exercises. 188 III Auslander-Reiten theory 203 1 The radical of a module category. 203 2 The Harada-Sai lemma. 207 3 The space of extensions. 209 4 The Auslander-Reiten translations. 232 5 The Nakayama functors. 247 6 The Auslander-Reiten formulas. 252 7 Irreducible and almost split homomorphisms . 257 8 Almost split sequences. 269 9 The Auslander-Reiten quiver. 282 10 The Auslander theorem. 301 viii Contents 11 The Bautista-Smal0 theorem. 312 12 Exercises. 314 IV Selfinjective algebras 332 1 The Frobenius theorem. 332 2 The Brauer-Nesbitt-Nakayama theorems. 336 3 Frobenius algebras. 345 4 Symmetric algebras. 355 5 Simple algebras. 368 6 The Nakayama theorems. 375 7 Non-Frobenius selfinjective algebras. 386 8 The syzygy functors . 392 9 The higher extension spaces. 402 10 Periodic modules. 414 11 Periodic algebras. 427 12 The Green-Snashall-Solberg theorems . 442 13 Dynkin and Euclidean graphs . 447 14 Canonical mesh algebras of Dynkin type. 452 15 The Riedtmann-Todorov theorem. 455 16 Exercises. 470 V Hecke algebras 489 1 Finite reflection groups. 489 2 Coxeter graphs. 499 3 The Coxeter theorems . 507 4 The Iwahori theorem. 515 5 Hecke algebras. 528 6 Exercises. 533 VI Hopf algebras 539 1 Coalgebras. 539 2 Hopfalgebras. 552 3 The Larson-Sweedler theorems . 584 4 The Radford theorem. 595 5 The Fischman-Montgomery-Schneider formula. 609 6 The module category. 616 7 Exercises. 630 Bibliography 637 Index 645
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author	Skowroński, Andrzej 1950-2020 Yamagata, Kunio
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isbn	9783037191026
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spelling	Skowroński, Andrzej 1950-2020 Verfasser (DE-588)141208694 aut Frobenius Algebras 1 Basic representation theory Andrzej Skowroński, Kunio Yamagata Zürich European Mathematical Society 2011 XI, 650 Seiten txt rdacontent n rdamedia nc rdacarrier Hopf-Algebra (DE-588)4160646-2 gnd rswk-swf Hecke-Algebra (DE-588)4159341-8 gnd rswk-swf Frobenius-Algebra (DE-588)4155476-0 gnd rswk-swf Frobenius-Algebra (DE-588)4155476-0 s Hecke-Algebra (DE-588)4159341-8 s Hopf-Algebra (DE-588)4160646-2 s DE-604 Yamagata, Kunio Verfasser (DE-588)1022466070 aut (DE-604)BV042009165 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027451058&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Skowroński, Andrzej 1950-2020 Yamagata, Kunio Frobenius Algebras Hopf-Algebra (DE-588)4160646-2 gnd Hecke-Algebra (DE-588)4159341-8 gnd Frobenius-Algebra (DE-588)4155476-0 gnd
subject_GND	(DE-588)4160646-2 (DE-588)4159341-8 (DE-588)4155476-0
title	Frobenius Algebras
title_auth	Frobenius Algebras
title_exact_search	Frobenius Algebras
title_full	Frobenius Algebras 1 Basic representation theory Andrzej Skowroński, Kunio Yamagata
title_fullStr	Frobenius Algebras 1 Basic representation theory Andrzej Skowroński, Kunio Yamagata
title_full_unstemmed	Frobenius Algebras 1 Basic representation theory Andrzej Skowroński, Kunio Yamagata
title_short	Frobenius Algebras
title_sort	frobenius algebras basic representation theory
topic	Hopf-Algebra (DE-588)4160646-2 gnd Hecke-Algebra (DE-588)4159341-8 gnd Frobenius-Algebra (DE-588)4155476-0 gnd
topic_facet	Hopf-Algebra Hecke-Algebra Frobenius-Algebra
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027451058&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV042009165
work_keys_str_mv	AT skowronskiandrzej frobeniusalgebras1 AT yamagatakunio frobeniusalgebras1

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