Abstract
Let g = g0 + g1 be a basic Lie superalgebra over ℂ, and e a minimal nilpotent element in g0. Set W’x to be the refined W-superalgebra associated with the pair (g; e), which is called a minimal W-superalgebra. In this paper we present a set of explicit generators of minimal W-superalgebras and the commutators between them. By virtue of this, we show that over an algebraically closed field k of characteristic p»0, the lower bounds of dimensions in the modular representations of basic Lie superalgebras with minimal nilpotent p-characters are attainable. Such lower bounds are indicated in [33] as the super Kac{Weisfeiler property.
| Original language | English |
|---|---|
| Pages (from-to) | 123-188 |
| Number of pages | 66 |
| Journal | Publications of the Research Institute for Mathematical Sciences |
| Volume | 55 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2019 |
| Externally published | Yes |
Keywords
- (super) kac{weisfeiler conjecture (property) for modular lie (super)algebras
- Basic (classical) lie superalgebras
- Finite w-(super)algebras
- Minimal nilpo- tent elements
- Modular representations of lie (super)algebras