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On Self‐Contragredient Genera Of Z[ G ]‐Lattices
Author(s) -
Neiße Olaf,
Weiss Alfred
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609302001595
Subject(s) - mathematics , lattice (music) , combinatorics , pure mathematics , physics , acoustics
If G is a finite group and V is a finite‐dimensional Q[ G ]‐module, V is isomorphic to its contragredient module V *. In general, V need not contain any Z[ G ]‐lattice which is locally isomorphic to its contragredient lattice. Nevertheless, it turns out that for every V there exists another Q[ G ]‐module V′ such that both V ′ and V ⊗ V ′ contain Z[ G ]‐lattices which are locally isomorphic to their contragredient lattices. 2000 Mathematics Subject Classification 20C10, 20C05.