Auslander-Reiten theory revisited
Osamu Iyama
TL;DR
This paper revisits classical Auslander-Reiten theory for finite-dimensional algebras, introduces higher concepts like n-cluster tilting subcategories, and explores their properties with illustrative examples.
Contribution
It extends Auslander-Reiten theory to higher dimensions through n-cluster tilting subcategories and higher almost split sequences, providing new insights and examples.
Findings
Extended Auslander-Reiten theory to n-cluster tilting subcategories
Introduced higher almost split sequences and Auslander algebras
Provided multiple illustrative examples
Abstract
We recall several results in Auslander-Reiten theory for finite-dimensional algebras over fields and orders over complete local rings. Then we introduce -cluster tilting subcategories and higher theory of almost split sequences and Auslander algebras there. Several examples are explained.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons