On the description of Leibniz superalgebras of nilindex n+m

Abstract

In this work we investigate the complex Leibniz superalgebras with characteristic sequence (n1, . . . , nk|m) and nilindex n + m, where n = n1 + · · ·+nk, n and m (m 6= 0) are dimensions of even and odd parts, respectively. Such superalgebras with condition n1 ≥ n − 1 were classified in [4]–[5]. Here we prove that in the case n1 ≤ n − 2 the Leibniz superalgebras have nilindex less than n +m. Thus, we get the classification of Leibniz superalgebras with characteristic sequence (n1, . . . , nk|m) and nilindex n +m.