Auslander-Reiten theory in a Krull-Schmidt category
نویسندگان
چکیده
منابع مشابه
Auslander-Reiten theory in a Krull-Schmidt category
We first introduce the notion of an Auslander-Reiten sequence in a Krull-Schmidt category. This unifies the notion of an almost split sequence in an abelian category and that of an Auslander-Reiten triangle in a triangulated category. We then define the Auslander-Reiten quiver of a Krull-Schmidt category and describe the shapes of its semi-stable components. The main result generalizes those fo...
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We recall several results in Auslander-Reiten theory for finite-dimensional algebras over fields and orders over complete local rings. Then we introduce n-cluster tilting subcategories and higher theory of almost split sequences and Auslander algebras there. Several examples are explained. Mathematics Subject Classification (2000). Primary 16G70; Secondary 16E30, 16G30.
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First, for a general Krull-Schmidt category, we provide criteria for an Auslander-Reiten component with sections to be standard. Specializing to the category of finitely presented representations of a strongly locally finite quiver and its bounded derived category, we obtain many new types of standard Auslander-Reiten components. Finally, specialized to the module category of a finite-dimension...
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Article history: Received 8 July 2015 Received in revised form 22 February 2016 Available online 4 August 2016 Communicated by S. Koenig We investigate how the higher almost split sequences over a tensor product of algebras are related to those over each factor. Herschend and Iyama give in [6] a criterion for when the tensor product of an n-representation finite algebra and an m-representation ...
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We develop an Auslander-Reiten theory for triangulated categories which is based on Brown’s representability theorem. In a fundamental article [3], Auslander and Reiten introduced almost split sequences for the category of finitely generated modules over an artin algebra. These are short exact sequences which look almost like split exact sequences, but many authors prefer to call them Auslander...
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ژورنال
عنوان ژورنال: The São Paulo Journal of Mathematical Sciences
سال: 2010
ISSN: 2316-9028,1982-6907
DOI: 10.11606/issn.2316-9028.v4i3p425-472