ON THE CLASSIFICATION OF COMPLEX LEIBNIZ SUPERALGEBRAS WITH CHARACTERISTIC SEQUENCE (n - 1, 1 | m<sub>1</sub>, …, m<sub>k</sub>) AND NILINDEX n + m
Sergio AlbeverioInstitut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, D-53115 Bonn, GermanyB. A. OmirovInstitute of Mathematics and Information Technologies, Uzbekistan Academy of Science, F. Hodjaev str. 29, 100125, Tashkent, UzbekistanAbror KhudoyberdiyevInstitute of Mathematics and Information Technologies, Uzbekistan Academy of Science, F. Hodjaev str. 29, 100125, Tashkent, Uzbekistan
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Abstract
In this work we investigate the complex Leibniz superalgebras with characteristic sequence (n - 1, 1|m 1 , …, m k ) and with nilindex equal to n + m. We prove that such superalgebras with the condition m 2 ≠ 0 have nilindex less than n + m. Therefore the complete classification of Leibniz algebras with characteristic sequence (n - 1, 1|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].
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