2017/07/12 by Helen Samara Dos Santos, Santos, Helen Samara Dos, Caio De Naday Hornhardt +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #16W55 #17A70 (Secondary) #17B70 (Primary) 16W50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Sphingolipid Metabolism and Signaling
paper · pdf · doi:10.48550/arxiv.1707.03932
openalex publication_date 2017/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We classify gradings by arbitrary abelian groups on the classical simple Lie superalgebras P(n), n ≥ 2, and on the simple associative superalgebras M(m,n), m, n ≥ 1, over an algebraically closed field: fine gradings up to equivalence and G-gradings, for a fixed group G, up to isomorphism. As a corollary, we also classify up to isomorphism the G-gradings on the classical Lie superalgebra A(m,n) that are induced from G-gradings on M(m+1,n+1). In the case of Lie superalgebras, the characteristic is assumed to be 0.