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A remark on Rickard complexes (1305.4945v1)
Published 21 May 2013 in math.RT
Abstract: In this paper, we characterize a Rickard complex, which induces a Rickard equivalence between the block algebras of a block $b$ and its Brauer correspondent and whose vertices have the same order as defect groups of the block $b$. The homology of such a Rickard complex vanishes at all degree but degree $q$, and the homology at degree $q$ induces a basic Morita equivalence between the block algebras in the sense of Puig.
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