Khudoyberdiyev A. Kh. ; Muratova Kh. A - Solvable Leibniz superalgebras whose nilradical has the characteristic sequence $(n-1, 1 \mid m)$ and nilindex $n+m$

cm:11369 - Communications in Mathematics, September 20, 2023, Volume 32 (2024), Issue 2 (Special issue: CIMPA schools "Nonassociative Algebras and related topics, Brazil'2023" and "Current Trends in Algebra, Philippines'2024") - https://doi.org/10.46298/cm.11369
Solvable Leibniz superalgebras whose nilradical has the characteristic sequence $(n-1, 1 \mid m)$ and nilindex $n+m$Article

Authors: Khudoyberdiyev A. Kh. ; Muratova Kh. A

    Leibniz superalgebras with nilindex $n + m$ and characteristic sequence $(n-1, 1 \ | \ m)$ divided into four parametric classes that contain a set of non-isomorphic superalgebras. In this paper, we give a complete classification of solvable Leibniz superalgebras whose nilradical is a nilpotent Leibniz superalgebra with nilindex $n + m$ and characteristic sequence $(n-1, 1 \ | \ m)$. We obtain a condition for the value of parameters of the classes of such nilpotent superalgebras for which they have a solvable extension. Moreover, the classification of solvable Leibniz superalgebras whose nilradical is a Lie superalgebra with the maximal nilindex is given.


    Volume: Volume 32 (2024), Issue 2 (Special issue: CIMPA schools "Nonassociative Algebras and related topics, Brazil'2023" and "Current Trends in Algebra, Philippines'2024")
    Published on: September 20, 2023
    Accepted on: June 27, 2023
    Submitted on: May 25, 2023
    Keywords: Mathematics - Rings and Algebras,17A32, 17A36, 17B30

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