Self-dual lattices for maximal orders in group algebras

Gluck, David

doi:10.1090/S0002-9939-1985-0770524-8

Self-dual lattices for maximal orders in group algebras
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by David Gluck PDF

Proc. Amer. Math. Soc. 93 (1985), 221-224 Request permission

Abstract:

Let $G$ be a finite group and $V$ an irreducible ${\mathbf {Q}}[G]$-module. Let $R$ be a Dedekind domain with quotient field ${\mathbf {Q}}$ such that $\left | G \right |$ is a unit in $R$. For applications to topology it is of interest to know if $V$ contains a full self-dual $R[G]$-lattice. We show that such lattices always exist for some major classes of finite groups.

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