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Irreducible modules of modular Lie superalgebras and super version of the first Kac–Weisfeiler conjecture
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- Journal:
- Canadian Mathematical Bulletin / Volume 67 / Issue 3 / September 2024
- Published online by Cambridge University Press:
- 11 December 2023, pp. 554-573
- Print publication:
- September 2024
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Suppose
$\mathfrak {g}=\mathfrak {g}_{\bar 0}+\mathfrak {g}_{\bar 1}$ is a finite-dimensional restricted Lie superalgebra over an algebraically closed field 
$\mathbf {k}$ of characteristic 
$p>2$. In this article, we propose a conjecture for maximal dimensions of irreducible modules over the universal enveloping algebra 
$U(\mathfrak {g})$ of 
$\mathfrak {g}$, as a super generalization of the celebrated first Kac–Weisfeiler conjecture. It is demonstrated that the conjecture holds for all basic classical Lie superalgebras and all completely solvable restricted Lie superalgebras. In this process, we investigate irreducible representations of solvable Lie superalgebras.
THE GENERALIZED WITT MODULAR LIE SUPERALGEBRA OF CARTAN TYPE
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- Journal:
- Journal of the Australian Mathematical Society / Volume 91 / Issue 2 / October 2011
- Published online by Cambridge University Press:
- 18 November 2011, pp. 145-162
- Print publication:
- October 2011
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We construct the generalized Witt modular Lie superalgebra
of Cartan type. We give a set of generators for and show that is an extension of a subalgebra of by an ideal 
. Finally, we describe the homogeneous derivations of Z-degree of and we determine the derivation superalgebra of .
of Cartan type. We give a set of generators for 
. Finally, we describe the homogeneous derivations of 