Representation theory [Documento electrónico] : a homological algebra point of view / Alexander Zimmermann
Language: eng.Country: Germany.Publication: Cham : Springer International Publishing, 2014Description: XX, 707 p. : il.ISBN: 978-3-319-07968-4.Series: Algebra and ApplicationsSubject - Topical Name: Representações de grupos | Álgebra homológica Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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QA176.SPR FCT 80867 Groups and symmetries, from finite groups to Lie groups | QA176.SPR FCT 80973 Representation theory of algebraic groups and quantum groups | QA176.SPR FCT 81625 Symmetry , representation theory and its applications, in honor of Nolan R. Wallach | QA176.SPR FCT 82052 Representation theory, a homological algebra point of view | QA176.SPR FCT 82252 Blocks and families for cyclotomic Hecke algebras | QA176.SPR FCT 94499 Dirac operators in representation theory | QA177.SPR FCT 81081 Representations of SL2(Fq) |
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Introducing the representation theory of groups and finite dimensional algebras, this book first studies basic non-commutative ring theory, covering the necessary background of elementary homological algebra and representations of groups to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields, and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.
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