Group gradings on classical Lie superalgebras

2025/06/28 by Caio De Naday Hornhardt, Hornhardt, Caio De Naday, Mikhail Kochetov +1 · 1 citation
Mathematics · #16W10 (Secondary) #16W50 #17B70 (Primary) 16W55 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2506.23037

openalex publication_date 2025/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Special pure gradings on simple Lie algebras of types E₆, E₇, E₈

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