On simple modules for the restricted Lie superalgebra $gl(m|n)$
Chaowen Zhang
TL;DR
This paper investigates the structure of simple modules for the restricted Lie superalgebra gl(m|n), providing conditions for simplicity and establishing an analogue of the Kac-Weisfeiler theorem.
Contribution
It introduces new criteria for the simplicity of modules and extends the Kac-Weisfeiler theorem to the superalgebra setting.
Findings
Conditions for module simplicity are established.
An analogue of the Kac-Weisfeiler theorem is proved.
Results advance understanding of representation theory for gl(m|n).
Abstract
In this paper, we study the simple modules for the restricted Lie superalgebra . A condition for the simplicity of the induced modules is given, and an analogue of Kac-Weisfeiler theorem is proved.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons