On Morita theory for self-dual modules

Details On Morita theory for self-dual modules On Morita theory for self-dual modules

2008-03-25

arxiv.org/abs/0803.3580v1

Mathematics

Representation Theory

Scientific paper

Let $G$ be a finite group and let $k$ be a field of characteristic $p$. It is known that a $kG$-module $V$ carries a non-degenerate $G$-invariant bilinear form $b$ if and only if $V$ is self-dual. We show that whenever a Morita bimodule $M$ which induces an equivalence between two blocks $B(kG)$ and $B(kH)$ of group algebras $kG$ and $kH$ is self-dual then the correspondence preserves self-duality. Even more, if the bilinear form on $M$ is symmetric then for $p$ odd the correspondence preserves the geometric type of simple modules. In characteristic 2 this holds also true for projective modules.

Affiliated with

Also associated with

No associations

Rating

On Morita theory for self-dual modules does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Morita theory for self-dual modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Morita theory for self-dual modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-349326