Ebook: Finite Dimensional Algebras and Related Topics

Based on invited lectures at the 1992 Canadian Algebra Seminar, this volume represents an up-to-date and unique report on finite-dimensional algebras as a subject with many serious interactions with other mathematical disciplines, including algebraic groups and Lie theory, automorphic forms, sheaf theory, finite groups, and homological algebra. It will interest mathematicians and graduate students in these and related subjects as an introduction to research in an area of increasing relevance and importance.

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Based on invited lectures at the 1992 Canadian Algebra Seminar, this volume represents an up-to-date and unique report on finite-dimensional algebras as a subject with many serious interactions with other mathematical disciplines, including algebraic groups and Lie theory, automorphic forms, sheaf theory, finite groups, and homological algebra. It will interest mathematicians and graduate students in these and related subjects as an introduction to research in an area of increasing relevance and importance.

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Based on invited lectures at the 1992 Canadian Algebra Seminar, this volume represents an up-to-date and unique report on finite-dimensional algebras as a subject with many serious interactions with other mathematical disciplines, including algebraic groups and Lie theory, automorphic forms, sheaf theory, finite groups, and homological algebra. It will interest mathematicians and graduate students in these and related subjects as an introduction to research in an area of increasing relevance and importance.

Content:
Front Matter....Pages i-xiv
Equivalences of Blocks of Group Algebras....Pages 1-26
On the Endomorphism Algebras of Gelfand-Graev Representations....Pages 27-35
Harish-Chandra Vertices, Green Correspondence in Hecke Algebras, and Steinbergs Tensor Product Theorem in Nondescribing Characteristic....Pages 37-57
On Tilting Modules and Invariants for Algebraic Groups....Pages 59-77
Harish-Chandra Subalgebras and Gelfand-Zetlin Modules....Pages 79-93
Algebras Associated to Bruhat Intervals and Polyhedral Cones....Pages 95-121
Symmetric Groups and Quasi-Hereditary Algebras....Pages 123-161
Quasitilted Algebras....Pages 163-181
Tilting Theory and Differential Graded Algebras....Pages 183-190
Wild Canonical Algebras and Rings of Automorphic Forms....Pages 191-212
The Ext Algebra of a Highest Weight Category....Pages 213-222
Coxeter transformations and the representation theory of algebras....Pages 223-253
Translation Functors and Equivalences of Derived Categories for Blocks of Algebraic Groups....Pages 255-264
Blocks with cyclic defect (Green orders)....Pages 265-276
Rigid and Exceptional Sheaves on a Del Pezzo Surface....Pages 277-291
Quasihereditary algebras and Kazhdan-Lusztig theory....Pages 293-308
Cycles in Module Categories....Pages 309-345
Relative Homology....Pages 347-359
Tilting Theory and Selfinjective Algebras....Pages 361-390

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Based on invited lectures at the 1992 Canadian Algebra Seminar, this volume represents an up-to-date and unique report on finite-dimensional algebras as a subject with many serious interactions with other mathematical disciplines, including algebraic groups and Lie theory, automorphic forms, sheaf theory, finite groups, and homological algebra. It will interest mathematicians and graduate students in these and related subjects as an introduction to research in an area of increasing relevance and importance.

Content:
Front Matter....Pages i-xiv
Equivalences of Blocks of Group Algebras....Pages 1-26
On the Endomorphism Algebras of Gelfand-Graev Representations....Pages 27-35
Harish-Chandra Vertices, Green Correspondence in Hecke Algebras, and Steinbergs Tensor Product Theorem in Nondescribing Characteristic....Pages 37-57
On Tilting Modules and Invariants for Algebraic Groups....Pages 59-77
Harish-Chandra Subalgebras and Gelfand-Zetlin Modules....Pages 79-93
Algebras Associated to Bruhat Intervals and Polyhedral Cones....Pages 95-121
Symmetric Groups and Quasi-Hereditary Algebras....Pages 123-161
Quasitilted Algebras....Pages 163-181
Tilting Theory and Differential Graded Algebras....Pages 183-190
Wild Canonical Algebras and Rings of Automorphic Forms....Pages 191-212
The Ext Algebra of a Highest Weight Category....Pages 213-222
Coxeter transformations and the representation theory of algebras....Pages 223-253
Translation Functors and Equivalences of Derived Categories for Blocks of Algebraic Groups....Pages 255-264
Blocks with cyclic defect (Green orders)....Pages 265-276
Rigid and Exceptional Sheaves on a Del Pezzo Surface....Pages 277-291
Quasihereditary algebras and Kazhdan-Lusztig theory....Pages 293-308
Cycles in Module Categories....Pages 309-345
Relative Homology....Pages 347-359
Tilting Theory and Selfinjective Algebras....Pages 361-390
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