Auslander-Reiten theory over topological spaces
نویسندگان
چکیده
منابع مشابه
Auslander-reiten Triangles and Quivers over Topological Spaces
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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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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Let X be a smooth projective scheme of dimension d ≥ 1 over the field k, and let C be an indecomposable coherent sheaf on X . Then there is an Auslander-Reiten sequence in the category of quasi-coherent sheaves on X , 0 → (ΣC)⊗ ω −→ B −→ C → 0. Here ΣC is the (d−1)’st syzygy in a minimal injective resolution of C, and ω is the dualizing sheaf of X . 0. Introduction This note shows that Auslande...
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ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2004
ISSN: 0010-2571,1420-8946
DOI: 10.1007/s00014-001-0795-4