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Journal of the London Mathematical Society Advance Access originally published online on October 25, 2007
Journal of the London Mathematical Society 2007 76(3):567-585; doi:10.1112/jlms/jdm065
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© 2007 London Mathematical Society

Constructions of stable equivalences of Morita type for finite-dimensional algebras III

Yuming Liu and Changchang Xi

School of Mathematical Sciences
Beijing Normal University
100875 Beijing
PR China
liuym2{at}263.net

In this paper, we provide a new method to produce stable equivalences of Morita type. Our main results can be stated as follows. Let A and B be two finite-dimensional k-algebras over a field k. Suppose that two bimodules AMB and BNA define a stable equivalence of Morita type between A and B and that R is a generator for A-modules. Then there is a stable equivalence of Morita type defined by X and Y between the endomorphism algebra EndA(R) of the module R and the endomorphism algebra EndB(N{otimes}AR) of the module N{otimes}AR. If M and N satisfy the property that both (N{otimes}A–, M{otimes}B–) and (M{otimes}B–, N{otimes}A–) are adjoint pairs of functors, then so do the modules X and Y. Moreover, we show that the self-injective dimension and the Gorenstein property are invariant under stable equivalences of Morita type with the above-mentioned adjoint property.

Dedicated to Professor Zhexian Wan on the occasion of his 80th birthday

2000 Mathematics Subject Classification 16G10, 16E30, 16G70, 18G05, 20J05.

The authors acknowledge gratefully the support from CFKSTIP (No. 704004) and the Doctor Program Foundation (no. 20040027002), Ministry of Education of China, and the partial support from NSFC.

Received May 16, 2006; published online October 25, 2007.


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