\(\mathbb{W}^t\)-approximation representations over quasi \(k\)-Gorenstein algebras
For any positive integer \(k\) Auslander introduced the notion of \(k\)-Gorenstein algebra in the non-commutative case and proved that the \(k\)-Gorenstein algebras are left-right symmetric. Then \textit{M. Auslander} and \textit{I. Reiten} studied the homological finiteness of categories of modules over \(k\)-Gorenstein algebras [see J. Pure Appl. Algebra 92, No. 1, 1-27 (1992; Zbl 0803.16016)]. In the paper under review the author introduces first the notion of quasi \(k\)-Gorenstein algebra and shows by examples that this notion deserves to be studied (in particular, unlike in the \(k\)-Gorenstein case, the quasi \(k\)-Gorenstein algebras are not always left-right symmetric). Then, in connection with a series of papers by M. Auslander and I. Reiten on the representation theory of Artin algebras, he defines and studies the notion of \(\mathbb{W}^t\)-approximation representation. Some applications to homologically finite subcategories are given. This paper is based on a part of the author's Ph.D. thesis.
scientific article; zbMATH DE number 1439324