Group gradings on classical Lie superalgebras

Caio De Naday Hornhardt; Mikhail Kochetov

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arXiv · 2506.23037

Group gradings on classical Lie superalgebras

Caio De Naday Hornhardt·Mikhail Kochetov

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Abstract

We classify, up to isomorphism, the group gradings on the non-exceptional classical simple Lie superalgebras, except for type A(1,1), over an algebraically closed field of characteristic zero. To this end, we study graded-simple and graded-superinvolution-simple associative superalgebras satisfying the descending chain condition on graded left superideals, which allows us to classify abelian group gradings on finite-dimensional simple and superinvolution-simple associative superalgebras over an algebraically closed field of characteristic different from 2.

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Caio De Naday Hornhardt, Mikhail Kochetov. 2025-06-28. Group gradings on classical Lie superalgebras. https://arxiv.org/abs/2506.23037

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