Trends in Representation Theory of Algebras and Related Topics

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pp: 349–397

DOI: 10.4171/062-1/8

Auslander–Reiten theory revisited

Osamu Iyama[1]

(1) Graduate School of Mathematics, Nagoya University, Furocho, Chikusa-ku, 464-8602, NAGOYA, JAPAN

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. Several examples are explained.

Keywords: Auslander–Reiten theory, n-cluster tilting subcategory, n-Auslander algebra, n-almost split sequence