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ON SELF-CONTRAGREDIENT GENERA OF ${\bb Z}[G]$-LATTICES

Published online by Cambridge University Press:  20 March 2003

OLAF NEIßE
Affiliation:
Institut für Mathematik, Universität Augsburg, Universitätsstraße 14, D-86135 Augsburg, [email protected]
ALFRED WEISS
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, AB, T6G 2G1, [email protected]
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Abstract

If $G$ is a finite group and $V$ is a finite-dimensional ${\rm Q\!\!\!I}\,[G]$-module, $V$ is isomorphic to its contragredient module $V^*$. In general, $V$ need not contain any ${\bb Z}[G]$-lattice which is locally isomorphic to its contragredient lattice. Nevertheless, it turns out that for every $V$ there exists another ${\rm Q\!\!\!I}\,[G]$-module $V^{\prime}$; such that both $V^{\prime}$; and $V \oplus V^{\prime}$; contain ${\bb Z}[G]$-lattices which are locally isomorphic to their contragredient lattices.

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Type
NOTES AND PAPERS
Copyright
© The London Mathematical Society 2003

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Footnotes

The authors acknowledge support provided by the DFG and by the NSERC.