Khudoyberdiyev A. Kh. ; Muratova Kh. A
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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")
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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
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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.