03280nam a22005295i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001600186072002300202082001200225100003600237245011600273264007500389300004300464336002600507337002600533338003600559347002400595490004700619505018500666520130600851650001702157650001302174650002302187650002102210650003502231650002502266650001802291650001702309650001302326650003602339650004202375650003802417710003402455773002002489776003602509830004702545856004802592912001402640999001902654952007702673978-3-319-07968-4DE-He21320180115171616.0cr nn 008mamaa140815s2014 gw | s |||| 0|eng d a97833190796849978-3-319-07968-47 a10.1007/978-3-319-07968-42doi 4aQA150-272 7aPBF2bicssc 7aMAT0020002bisacsh04a5122231 aZimmermann, Alexander.eauthor.10aRepresentation Theoryh[electronic resource] :bA Homological Algebra Point of View /cby Alexander Zimmermann. 1aCham :bSpringer International Publishing :bImprint: Springer,c2014. aXX, 707 p. 59 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aAlgebra and Applications,x1572-5553 ;v190 aRings, Algebras and Modules -- Modular Representations of Finite Groups -- Abelian and Triangulated Categories -- Morita theory -- Stable Module Categories -- Derived Equivalences. 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. 0aMathematics. 0aAlgebra. 0aAssociative rings. 0aRings (Algebra). 0aCategory theory (Mathematics). 0aHomological algebra. 0aGroup theory.14aMathematics.24aAlgebra.24aAssociative Rings and Algebras.24aCategory Theory, Homological Algebra.24aGroup Theory and Generalizations.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9783319079677 0aAlgebra and Applications,x1572-5553 ;v1940uhttp://dx.doi.org/10.1007/978-3-319-07968-4 aZDB-2-SMA c371453d371453 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK