The classification of Leibniz superalgebras of nilindex [formula omitted] ( [formula omitted

Abstract

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 ( n 1 , … , n k | m 1 , … , m s ) (where n 1 + ⋯ + n k = n , m 1 + ⋯ + m s = m ) for n 1 ⩾ n − 1 and ( n 1 , … , n k | 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 ( n 1 , … , n k | m 1 , … , m s ) , where n 1 ⩽ n − 2 and m 1 ⩽ m − 1 the Leibniz superalgebras have nilindex less than n + m . Thus, we complete the classification of Leibniz superalgebras with nilindex n + m .