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 language | English |
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Pages (from-to) | 288-299 |
Number of pages | 12 |
Journal | Journal of Algebra |
Volume | 414 |
Early online date | 16 Jun 2014 |
DOIs | |
Publication status | Published - 15 Sept 2014 |
Keywords
- modular representations
- elementary abelian groups
- Loewy length