Elements of the Representation Theory of Associative Algebras: Volume 1: Techniques of Representation TheoryCambridge University Press, 2006年2月13日 This first part of a two-volume set offers a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The authors present this topic from the perspective of linear representations of finite-oriented graphs (quivers) and homological algebra. The self-contained treatment constitutes an elementary, up-to-date introduction to the subject using, on the one hand, quiver-theoretical techniques and, on the other, tilting theory and integral quadratic forms. Key features include many illustrative examples, plus a large number of end-of-chapter exercises. The detailed proofs make this work suitable both for courses and seminars, and for self-study. The volume will be of great interest to graduate students beginning research in the representation theory of algebras and to mathematicians from other fields. |
常見字詞
A-homomorphism abelian categories additive category additive functor adjoint amalgammed sum B-module homomorphism calculation shows called categories Fun°PA category mod Cn+2 cochain complex Coker f cokernel commutative diagram composition of morphisms contravariant functor covariant functor defined as follows Definition denote direct sum dn+1 duality epimorphism equivalence of categories exact rows exists a unique extension Extn F is faithful finite dimensional K-algebra formula Fun°PA and Fun functor F functorial isomorphism functorial morphism global dimension HomA h1,N HomA(Pm HomA(Pm+1 Homc Home homomorphism identities 1x indecomposable injective resolution invertible jth summand K-category K-linear functor K-linear map K-vector spaces Kerp left A-module Lemma max pd modules in mod morphism h objects X1 p₁ phism projective resolution Proof quotient r.gl.dim rade rep(AMB representation-finite set of morphisms short exact sequence subfunctor Theorem triple two-sided ideal unique morphism vector zero