INVARIANTS UNDER STABLE EQUIVALENCES OF MORITA TYPE

The aim of this article is to study some invariants of associative algebras under stable equivalences of Morita type. First of all, we show that, if two finite-dimensional selfinjective k-algebras are stably equivalent of Morita type, then their orbit algebras are isomorphic. Secondly, it is verifie...

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Bibliographic Details
Published in:Acta mathematica scientia 2012-03, Vol.32 (2), p.605-618
Main Author: 李方 孙隆刚
Format: Article
Language:English
Subjects:
16D90
16E30
16G10
Algebra
Associative
Equivalence
Invariants
K-代数
Mathematical analysis
Modules
Orbit algebra
Orbits
quasitilted algebra
repetitive algebra
Representations
stable equivalence of Morita type
不变量
关联代数
变性
应用程序
有限维
稳定等价
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Summary:The aim of this article is to study some invariants of associative algebras under stable equivalences of Morita type. First of all, we show that, if two finite-dimensional selfinjective k-algebras are stably equivalent of Morita type, then their orbit algebras are isomorphic. Secondly, it is verified that the quasitilted property of an algebra is invariant under stable equivalences of Morita type. As an application of this result, it is obtained that if an algebra is of finite representation type, then its tilted property is invariant under stable equivalences of Morita type; the other application to partial tilting modules is given in Section 4. Finally, we prove that when two finite-dimensional k-algebras are stably equivalent of Morita type, their repetitive algebras are also stably equivalent of Morita tvDe under cert..in conditions.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(12)60042-3