On Morita theory for self-dual modules
نویسندگان
چکیده
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.
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