Abstract
AbstractMorita equivalences provide a very strong relationship between two rings, and in particular their representation theory. However, one observes in examples similarities between module categories which are not given by a Morita equivalence. Nevertheless, a structural connection is reasonable. One of the possible connections is a stable equivalence. A stable equivalence is the weakest possible equivalence we study. We examine abstract equivalences as well as stable equivalences of Morita type. As application we give the structure theorem of blocks with cyclic defect group and Reiten’s theorem on the invariance of self-injectivity under stable equivalences.KeywordsMorita TypeStability EquationsMorita EquivalenceDefect GroupBrauer Tree AlgebrasThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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