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024 7 $a10.1007/978-3-319-07968-4
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100   $a20140815d2014      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aRepresentation theory $ea homological algebra point of view /$fby Alexander Zimmermann
205   $a1st ed. 2014.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014.
215   $a1 online resource (720 p.)
225 1 $aAlgebra and Applications,$x1572-5553 ;$v19
300   $aDescription based upon print version of record.
311   $a1-322-13709-9 
311   $a3-319-07967-0 
320   $aIncludes bibliographical references and index.
327   $aRings, Algebras and Modules -- Modular Representations of Finite Groups -- Abelian and Triangulated Categories -- Morita theory -- Stable Module Categories -- Derived Equivalences.
330   $a  Introducing the representation theory of groups and finite dimensional algebras, this book first studies basic non-commutative ring theory, covering the necessary background of elementary homological algebra and representations of groups to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given ? such as the structure of blocks of cyclic defect groups ? whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields, and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.
410  0$aAlgebra and Applications,$x1572-5553 ;$v19
606   $aAlgebra
606   $aAssociative rings
606   $aRings (Algebra)
606   $aCategories (Mathematics)
606   $aAlgebra, Homological
606   $aGroup theory
606   $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000
606   $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027
606   $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035
606   $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078
615  0$aAlgebra.
615  0$aAssociative rings.
615  0$aRings (Algebra)
615  0$aCategories (Mathematics)
615  0$aAlgebra, Homological.
615  0$aGroup theory.
615 14$aAlgebra.
615 24$aAssociative Rings and Algebras.
615 24$aCategory Theory, Homological Algebra.
615 24$aGroup Theory and Generalizations.
676   $a512.55
700   $aZimmermann$b Alexander$4aut$4http://id.loc.gov/vocabulary/relators/aut$061857
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910299976203321
996   $aRepresentation theory$91409869
997   $aUNINA