Auslander-Reiten triangles in subcategories
نویسندگان
چکیده
منابع مشابه
On Auslander-Reiten translates in functorially finite subcategories and applications
Functorially finite subcategories in module categories over Artin algebras have been introduced by Auslander and Smalø [2] to provide a convenient setting for existence of relative Auslander-Reiten sequences in subcategories. Given a functorially finite subcategory, it is generally not well understood how to compute approximations, and the end terms of relative Auslander-Reiten sequences. In th...
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We introduce the concept of maximal orthogonal subcategories over artin algebras and orders, and develop higher Auslander-Reiten theory on them. Auslander-Reiten theory, especially the concept of almost split sequences and their existence theorem, is fundamental to study categories which appear in representation theory, for example, modules over artin algebras [ARS][GR][Ri], their functorially ...
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In this paper, Auslander-Reiten triangles are introduced into algebraic topology, and it is proved that their existence characterizes Poincaré duality spaces. Invariants in the form of quivers are also introduced, and Auslander-Reiten triangles and quivers over spheres are computed. The quiver over the d-dimensional sphere turns out to consist of d − 1 components, each isomorphic to ZA∞. So qui...
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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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ژورنال
عنوان ژورنال: Journal of K-theory
سال: 2008
ISSN: 1865-2433,1865-5394
DOI: 10.1017/is008007021jkt056