Hostname: page-component-7479d7b7d-8zxtt Total loading time: 0 Render date: 2024-07-11T08:29:59.279Z Has data issue: false hasContentIssue false

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, Germanyolaf.neisse@math.uni-augsburg.de
ALFRED WEISS
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, AB, T6G 2G1, Canadaaweiss@math.ualberta.ca
Get access

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.

Keywords

Type
NOTES AND PAPERS
Copyright
© The London Mathematical Society 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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