On constructing stably equivalent functors. (English) Zbl 0810.16013
Let \(A\) be an Artin algebra, and denote by \(T(A)\) the trivial extension of \(A\) by its minimal injective cogenerator. Let \(T_ A\) be a generalized tilting module [c.f. Y. Miyashita [Math. Z. 193, 113- 146 (1986; Zbl 0578.16015)] and set \(B = \text{End}(T_ A)\). It is shown that if either \(A\) or \(B\) is representation-finite, then \(T(A)\) and \(T(B)\) are stably equivalent. This comes as a corollary of some more detailed considerations too technical to reproduce here.
Reviewer: W.H.Gustafson (Lubbock)
MSC:
| 16G10 | Representations of associative Artinian rings |
| 16D90 | Module categories in associative algebras |
| 16G60 | Representation type (finite, tame, wild, etc.) of associative algebras |
| 16E30 | Homological functors on modules (Tor, Ext, etc.) in associative algebras |
Keywords:
stable equivalence; Artin algebra; trivial extension; minimal injective cogenerator; generalized tilting module; representation-finiteReferences:
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