On split regular Hom-Lie superalgebras

Matching Hom-Setting of Rota-Baxter Algebras, Dendriform Algebras, and Pre-Lie Algebras

“…It is shown that a Homassociative algebra gives rise to a Hom-Lie algebra using the commutator. Since then, various Hom-analogues of some classical algebraic structures have been introduced and studied intensively, such as Hom-coalgebras, Hom-bialgebras and Hom-Hopf algebras [24,25], Hom-groups [26,27], Hom-Hopf modules [28], Hom-Lie superalgebras [29,30], generalize Hom-Lie algebras [31], and Hom-Poisson algebras [32].…”

On the structure of split regular Hom-Lie–Rinehart algebras

“…Determining the structure of split algebras will become more and more meaningful in the area of research in mathematical physics. Recently,in [1,2,4,5,6,7,8,9,10,11,12], the structure of different classes of split algebras have been determined by the techniques of connections of roots.In the present paper we introduce the class of split regular Hom-Lie Rinehart algebras as the natural extension of the one of split Lie-Rinehart algebras and so of split regular Hom-Lie algebras, and study its tight structures based on some work in [1] and [3]. In section 2, we establish the preliminaries on split regular Hom-Lie Rinehart algebras theory.…”

On split regular BiHom-Poisson superalgebras

“…Determining the structure of split algebras will become more and more meaningful in the area of research in mathematical physics. Recently,[2][3][4][5][6][7][8], [9]-[11], [22]-[23]), the structure of different classes of split algebras have been determined by the techniques of connections of roots. The purpose of this paper is to consider the class of split regular BiHom-Poisson superalgebras, which is a natural extension of split regular BiHom-Lie superalgebras and split Hom-Lie superalgebras.In Section 2, we prove that such an arbitrary split regular BiHom-Poisson superalgebras A is of the form A = U + α I α with U a subspace of a maximal abelian subalgebra H and any I α , a well described ideal of A, satisfying [I α , I β ] + I α I β = 0 if [α] = [β].In Section 3, we present that under certain conditions, in the case of A being of maximal length, the simplicity of the algebra is characterized.…”

“…Determining the structure of split algebras will become more and more meaningful in the area of research in mathematical physics. Recently,[2][3][4][5][6][7][8], [9]-[11], [22]-[23]), the structure of different classes of split algebras have been determined by the techniques of connections of roots. The purpose of this paper is to consider the class of split regular BiHom-Poisson superalgebras, which is a natural extension of split regular BiHom-Lie superalgebras and split Hom-Lie superalgebras.…”