ON THE CLASSIFICATION OF COMPLEX LEIBNIZ SUPERALGEBRAS WITH CHARACTERISTIC SEQUENCE (n-1, 1|m1,..., mk) AND NILINDEX n+m

In this work we investigate the complex Leibniz superalgebras with characteristic sequence (n-1, 1 vertical bar m(1,...,) m(k)) and with nilindex equal to n+m. We prove that such superalgebras with the condition m(2) not equal 0 have nilindex less than n+m. Therefore the complete classification of Leibniz algebras with characteristic sequence (n - 1, 1 vertical bar m(1,...,) m(k)) and with nilindex equal to n+m is reduced to the classification of filiform Leibniz superalgebras of nilindex equal to n+m, which was provided in [3, 7].