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024 7 $a10.1007/978-3-319-11475-0
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100   $a20141229d2015      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aIntroduction to the Representation Theory of Algebras /$fby Michael Barot
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015.
215   $a1 online resource (X, 179 p. 109 illus.) 
300   $aBibliographic Level Mode of Issuance: Monograph
311 08$a3-319-11474-3 
320   $aIncludes bibliographical references and indexes.
327   $aMatrix Problems -- Representations of Quivers -- Algebras -- Module Categories -- Elements of Homological Algebra -- The Auslander-Reiten Theory -- Knitting -- Combinatorial Invariants -- Indecomposables and Dimensions.
330   $aThis book gives a general introduction to the theory of representations of algebras. It starts with examples of classification problems of matrices under linear transformations and explains the three common setups: representation of quivers, modules over algebras and additive functors over certain categories. The main part is devoted to (i) module categories, presenting the unicity of the decomposition into indecomposable modules, the Auslander?Reiten theory and the technique of knitting; (ii) the use of combinatorial tools such as dimension vectors and integral quadratic forms; and (iii) deeper theorems such as Gabriel?s Theorem, the trichotomy and the Theorem of Kac ? all accompanied by further examples. Each section includes exercises to facilitate understanding. By keeping the proofs as basic and comprehensible as possible and introducing the three languages at the beginning, this book is suitable for readers from the advanced undergraduate level onwards and enables them to consult related, specific research articles.
606   $aAssociative rings
606   $aRings (Algebra)
606   $aCategories (Mathematics)
606   $aAlgebra, Homological
606   $aAlgebra
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   $aGeneral Algebraic Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/M1106X
615  0$aAssociative rings.
615  0$aRings (Algebra)
615  0$aCategories (Mathematics)
615  0$aAlgebra, Homological.
615  0$aAlgebra.
615 14$aAssociative Rings and Algebras.
615 24$aCategory Theory, Homological Algebra.
615 24$aGeneral Algebraic Systems.
676   $a512.9
700   $aBarot$b Michael$4aut$4http://id.loc.gov/vocabulary/relators/aut$0768297
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910299780803321
996   $aIntroduction to the Representation Theory of Algebras$91564850
997   $aUNINA