Khudoyberdiyev, Abror Kh.; Muratova, Khosiyat Solvable Leibniz superalgebras whose nilradical has the characteristic sequence \((n-1, 1 |m)\) and nilindex \(n+m\). (English) Zbl 07900709 Commun. Math. 32, No. 2, Paper No. 2, 28 p. (2024). A \(\mathbb{Z}_2\)-graded vector space (or vector superspace) \(V\) is a direct sum of vector spaces \(V_{\bar{0}}\) and \(V_{\bar{1}}\), whose elements are called even and odd, respectively. For a homogeneous element (that is a non-zero element) \(v\in V_\lambda\) with \(\lambda\in\mathbb{Z}_2\), \(|v|=\lambda\) is the degree of \(v\). A (right) Leibniz superalgebra is a \(\mathbb{Z}_2\)-graded vector space \(L=L_{\bar{0}}\oplus L_{\bar{1}}\) equipped with a bilinear map \([-,-] : L \times L \to L\), satisfying the following conditions: (i) \([L_\lambda,L_\mu]\subseteq L_{\lambda+\mu}\) for every \(\lambda,\mu\in \mathbb{Z}_2\),(ii) \([x,[y,z]]=[[x,y],z]-(-1)^{|y||z|} [[x,z],y]\) (super Leibniz identity), for every \(x,y,z\in L\). Note that the even part \(L_{\bar{0}}\) of a Leibniz superalgebra is a Leibniz algebra. Also, a Lie superalgebra is a Leibniz superalgebra which satisfies the graded antisymmetric identity \([x,y]=-(-1)^{|x||y|} [y,x]\). Hence Leibniz superalgebras are a generalization of both Leibniz algebras and Lie superalgebras. When a Leibniz superalgebra \(L=L_{\bar{0}}\oplus L_{\bar{1}}\) is of dimension \(n+m\) in which \(\dim L_{\bar{0}}=n\) and \(\dim L_{\bar{1}}=m\), we write \(\dim L=(n|m)\).In this paper, it is provided a classification of solvable Leibniz superalgebras whose nilradical has nilindex (nilpotency class) \(n + m\) and characteristic sequence \((n-1, 1|m)\). Specific values are obtained for the parameters of the classes of such nilpotent superalgebras for which they have a solvable extension. Reviewer: Hesam Safa (Bojnord) Cited in 1 Document MSC: 17A32 Leibniz algebras 17A36 Automorphisms, derivations, other operators (nonassociative rings and algebras) 17B30 Solvable, nilpotent (super)algebras Keywords:Leibniz algebras; Leibniz superalgebras; solvable superalgebras; nilradical; derivations; characteristic sequence; nilindex × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] S. Albeverio, S. Ayupov, and B. Omirov. On nilpotent and simple Leibniz algebras. Com-munications in Algebra, 33(1):159-172, 2005. · Zbl 1065.17001 [2] M. Alvarez and I. Kaygorodov. The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras. Journal of Algebra, 588:278-314, 2021. · Zbl 1483.17004 [3] J. Ancochea Bermúdez, R. Campoamor-Stursberg, and L. García Vergnolle. Solvable Lie algebras with naturally graded nilradicals and their invariants. Journal of Physics A, 39(6):1339-1355, 2006. · Zbl 1095.17003 [4] J. 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