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Stable Module Categories

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Representation Theory

Part of the book series: Algebra and Applications ((AA,volume 19))

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Abstract

Morita 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.

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Authors and Affiliations

  1. Département de Mathématiques LAMFA (UMR 7352 du CNRS), Université de Picardie, Amiens, France

    Alexander Zimmermann

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  1. Alexander Zimmermann
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Correspondence to Alexander Zimmermann .

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Zimmermann, A. (2014). Stable Module Categories. In: Representation Theory. Algebra and Applications, vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-07968-4_5

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