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Structure of generalized modular Lie superalgebras of \(S\)-type. (Chinese. English summary) Zbl 1438.17017

Summary: By determining the ideal of the polynomial algebra of simple element form, we obtained the combined superalgebraic ideal of the tensor product of the divided power algebra, the external algebra and the polynomial algebra, and the ideal of the generalized modular Lie superalgebra \(\tilde S\). Then we gave the nonsimplicity of generalized modular Lie superalgebra \(\tilde S\) and the necessary and sufficient conditions under which \(\tilde S\) was a restricted Lie superalgebra.

MSC:

17B50 Modular Lie (super)algebras
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