Infinite-dimensional modular Lie superalgebra \(\Omega\). (English) Zbl 1470.17012

Xu, Xiaoning; Mu, Bing

Abstr. Appl. Anal. 2013, Article ID 923101, 10 p. (2013).

Summary: All ad-nilpotent elements of the infinite-dimensional Lie superalgebra \(\Omega\) over a field of positive characteristic are determined. The natural filtration of the Lie superalgebra \(\Omega\) is proved to be invariant under automorphisms by characterizing ad-nilpotent elements. Then an intrinsic property is obtained by the invariance of the filtration; that is, the integers in the definition of \(\Omega\) are intrinsic. Therefore, we classify the infinite-dimensional modular Lie superalgebra \(\Omega\) in the sense of isomorphism.

MSC:

17B50	Modular Lie (super)algebras
17B65	Infinite-dimensional Lie (super)algebras
17B70	Graded Lie (super)algebras

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