Modules with small Loewy length

David Benson, Fergus Reid

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

A module of complexity c for E≅(Z/p)r in characteristic p has Loewy length at least (p−1)(r−c)+1. We study the case of equality. If p is odd, the only rank varieties possible are finite unions of linear subspaces of dimension c , and every such rank variety occurs. If p=2, the variety has to be equidimensional. If such a variety is a finite union of set theoretic complete intersections then it occurs for such a module, but otherwise the situation is unclear. Exterior algebras in any characteristic are also treated, and follow the same behaviour as the case p=2 above.
Original languageEnglish
Pages (from-to)288-299
Number of pages12
JournalJournal of Algebra
Volume414
Early online date16 Jun 2014
DOIs
Publication statusPublished - 15 Sep 2014

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Union
Set-theoretic Complete Intersection
Exterior Algebra
Module
Equality
Odd
Subspace

Keywords

  • modular representations
  • elementary abelian groups
  • Loewy length

Cite this

Modules with small Loewy length. / Benson, David; Reid, Fergus.

In: Journal of Algebra, Vol. 414, 15.09.2014, p. 288-299.

Research output: Contribution to journalArticle

Benson, David ; Reid, Fergus. / Modules with small Loewy length. In: Journal of Algebra. 2014 ; Vol. 414. pp. 288-299.
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