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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Self-dual lattices for maximal orders in group algebras


Author: David Gluck
Journal: Proc. Amer. Math. Soc. 93 (1985), 221-224
MSC: Primary 20C10; Secondary 20C05
MathSciNet review: 770524
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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\vert G \right\vert$ 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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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0770524-8
PII: S 0002-9939(1985)0770524-8
Article copyright: © Copyright 1985 American Mathematical Society