INVARIANTS UNDER STABLE EQUIVALENCES OF MORITA TYPE  

作　　者：李方 孙隆刚 

机构地区：[1]Department of Mathematics,Zhejiang University

出　　处：《Acta Mathematica Scientia》2012年第2期605-618,共14页数学物理学报（B辑英文版）

基　　金：Project supported by the National Natural Science Foundation of China(10871170);the Zhejiang Provincial Natural Science Foundation of China(D7080064);supported by the National Natural Science Foundation of China(10801117)

摘　　要：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.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.

关 键 词：Orbit algebra repetitive algebra stable equivalence of Morita type qua-sitilted algebra 

分 类 号：O153[理学—数学]