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Modular representations of Heisenberg algebras

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Volume
457
Identifiers
DOI: 10.1016/j.laa.2014.05.015
Keywords
  • Heisenberg Algebra
  • Irreducible Representation
Disciplines
  • Mathematics

Abstract

Abstract Let F be an arbitrary field and let h(n) be the Heisenberg algebra of dimension 2n+1 over F. It was shown by Burde that if F has characteristic 0 then the minimum dimension of a faithful h(n)-module is n+2. We show here that his result remains valid in prime characteristic p, as long as (p,n)≠(2,1). We construct, as well, various families of faithful irreducible h(n)-modules if F has prime characteristic, and classify these under suitable assumptions on F. Applications to matrix theory are given.

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