The classification of Leibniz superalgebras of nilindex n+m (m≠0)

In this paper we investigate the description of the complex Leibniz superalgebras with nilindex n+m, where n and m (m≠0) are dimensions of even and odd parts, respectively. In fact, such superalgebras with characteristic sequence equal to (n1,…,nk|m1,…,ms) (where n1+⋯+nk=n, m1+⋯+ms=m) for n1⩾n−1 and (n1,…,nk|m) were classified in works by Ayupov et al. (2009) [3], , Camacho et al. (2010) [4], , Camacho et al. (in press) [5], , Camacho et al. (in press) [6]. Here we prove that in the case of (n1,…,nk|m1,…,ms), where n1⩽n−2 and m1⩽m−1 the Leibniz superalgebras have nilindex less than n+m. Thus, we complete the classification of Leibniz superalgebras with nilindex n+m.