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The goal of this paper is to study the structure of split regular BiHom-Leiniz superalgebras, which is a natural generalization of split regular Hom-Leiniz algebras and split regular BiHom-Lie superalgebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular BiHom-Leiniz superalgebras $mathfrak{L}$ is of the form $mathfrak{L}=U+sum_{a}I_a$ with $U$ a subspace of a maximal abelian subalgebra $H$ and any $I_{a}$, a well described ideal of $mathfrak{L}$, satisfying $[I_a, I_b]= 0$ if $[a] eq [b]$. In the case of $mathfrak{L}$ being of maximal length, the simplicity of $mathfrak{L}$ is also characterized in terms of connections of roots.
In this paper, we introduce the notion of the Hom-Leibniz-Rinehart algebra as an algebraic analogue of Hom-Leibniz algebroid, and prove that such an arbitrary split regular Hom-Leibniz-Rinehart algebra $L$ is of the form $L=U+sum_gamma I_gamma$ with
We present the description up to isomorphism of Leibniz superalgebras with characteristic sequence $(n|m_1,...,m_k)$ and nilindex $n+m,$ where $m=m_1+ >...+m_k,$ $n$ and $m$ ($m eq 0$) are dimensions of even and odd parts, respectively.
In this work we investigate the complex Leibniz superalgebras with characteristic sequence $(n_1,...,n_k|m)$ and nilindex n+m, where $n=n_1+...+n_k,$ n and m (m is not equal to zero) are dimensions of even and odd parts, respectively. Such superalgeb
Along this paper we show that under certain conditions the method for describing of solvable Lie and Leibniz algebras with maximal codimension of nilradical is also extensible to Lie and Leibniz superalgebras, respectively. In particular, we totally
The aim of this paper is to study the structures of split regular Hom-Lie Rinehart algebras. Let $(L,A)$ be a split regular Hom-Lie Rinehart algebra. We first show that $L$ is of the form $L=U+sum_{[gamma]inGamma/thicksim}I_{[gamma]}$ with $U$ a vect