Auslander-Reiten theory in a Krull-Schmidt category
By Shiping Liu. 2010
72 citations recorded by the source corpus.
We rst introduce the notion of an Auslander-Reiten sequence in a Krull-Schmidt category. This uni es the notion of an almost split sequence in an abelian category and that of an Auslander-Reiten triangle in a triangulated category. We then de ne the Auslander-Reiten quiver of a Krull-Schmidt category and describe the shapes of its semi-stable components. The main result generalizes those for an artin algebra and specializes to an arbitrary triangulated categories, in particular to the derived category of bounded complexes of nitely generated modules over an artin algebra of nite global dimension.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/3cbb0e3a6897e9397a89f3db867aaafa8484e1ec
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In Algebra and Number Theory
In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- Auslander–Reiten theory in extriangulated categories (2018, background): “aded categories (e.g. [Jo1, S]), and commutative and non-commutative schemes (e.g. [GL, RV]). Also there are many references studying Auslander{Reiten theory in more general additive categories (e.g. [I, Liu]). Recently, the class of extriangulated categories was in introduced in [NP] as a simultane”
- Triangulated quotient categories revisited (2016, methodology): “Auslander-Reiten theory in a Krull-Schmidt category was established by Liu in [Liu].”