Minimal -Superalgebras and the Modular Representations of Basic Lie Superalgebras

  • Yang Zeng

    Nanjing Audit University, China
  • Bin Shu

    East China Normal University, Shanghai, China
Minimal $W$-Superalgebras and the Modular Representations of Basic Lie Superalgebras cover
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Abstract

Let be a basic Lie superalgebra over , and a minimal nilpotent element in . Set to be the refined -superalgebra associated with the pair , which is called a minimal -superalgebra. In this paper we present a set of explicit generators of minimal -superalgebras and the commutators between them. In virtue of this, we show that over an algebraically closed field of characteristic , the lower bounds of dimensions in the modular representations of basic Lie superalgebras with minimal nilpotent -characters are attainable. Such lower bounds are indicated in [33] as the super Kac–Weisfeiler property.

Cite this article

Yang Zeng, Bin Shu, Minimal -Superalgebras and the Modular Representations of Basic Lie Superalgebras. Publ. Res. Inst. Math. Sci. 55 (2019), no. 1, pp. 123–188

DOI 10.4171/PRIMS/55-1-5