On the description of Leibniz superalgebras of nilindex n + m

In this work we investigate complex Leibniz superalgebras with characteristic sequence .n ₁ nkjm/ and nilindex nCm, where n D n1C Cnk, n and m (m0) are dimensions of even and odd parts, respectively. Such superalgebras with the condition n1 ≥ n ^-1 were completely classified. In the present paper, we prove that in the case n1 ≤ n ^-2 the Leibniz superalgebras have nilindex less than n C m. Thus, we obtain the classification of Leibniz superalgebras with characteristic sequence .n1nkjm/ and nilindex n C m.