On Morita theory for self-dual modules - Mathematics > Representation TheoryReport as inadecuate




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Abstract: Let $G$ be a finite group and let $k$ be a field of characteristic $p$. It isknown that a $kG$-module $V$ carries a non-degenerate $G$-invariant bilinearform $b$ if and only if $V$ is self-dual. We show that whenever a Moritabimodule $M$ which induces an equivalence between two blocks $BkG$ and$BkH$ of group algebras $kG$ and $kH$ is self-dual then the correspondencepreserves self-duality. Even more, if the bilinear form on $M$ is symmetricthen for $p$ odd the correspondence preserves the geometric type of simplemodules. In characteristic 2 this holds also true for projective modules.



Author: Wolfgang Willems, Alexander Zimmermann LAMFA

Source: https://arxiv.org/







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