相关论文: Representations and O-operators of Hom-(pre)-Jacob…

The aim of this work is to introduce and study the notions of Hom-pre-Jordan algebra and Hom-J-dendriform algebra which generalize Hom-Jordan algebras. Hom-Pre-Jordan algebras are regarded as the underlying algebraic structures of the…

The purpose of this paper is to introduce an algebraic cohomology theory of left pre-Jacobi-Jordan algebras. We use the cohomological approach to study linear deformations of these algebras. We also introduce the notion of Nijenhuis…

Representations of Hom-Jacobi-Jordan algebras are studied. In particular, adjoint representations and trivial representations are studied in detail. Derivations and central extensions of Hom-Jacobi-Jordan algebras are also discussed as an…

Some results on (pre-)Jacobi-Jordan algebras and their representations are proved. Moreover, the notion of matched pairs and relative Rota-Baxter operators on these algebras are introduced and studied. The cohomology theory of relative…

Representations and relative Rota-Baxter operators with respect to representations of Hom-Leibniz Poisson algebras are introduced and studied. Some characterizations of these operators are obtained. The notion of matched pair and Nijenhuis…

In this paper, we introduce the notion of n-Hom-pre-Lie superalgebras. We investigate the representation theory of n-Hom-pre-Lie superalgebras and we give some related results and structures based on Rota-Baxter operators, O-operators and…

In this paper, first we recall the notion of Hom-Jordan superalgebras and study their representations. We define the Yang-Baxter equation in a Hom-Jordan superalgebra. Additionally, we extend the connections between $\mathcal {O}$-operators…

Weighted Rota-Baxter Jacobi-Jordan algebras and their representations are studied. Moreover, we consider weighted Rota-Baxter paired operators that are related to weighted Rota-Baxter Jacobi-Jordan algebras together with their…

In this paper, first we study dual representations and tensor representations of Hom-pre-Lie algebras. Then we develop the cohomology theory of Hom-pre-Lie algebras in term of the cohomology theory of Hom-Lie algebras. As applications, we…

We define and derive basic properties of the notion of Rota-Baxter operator on anti-flexible algebra. Starting from a Rota-Baxter operator on an anti-flexible algebra, we construct pre-anti-flexible algebra structure and associated…

In this paper, we recall the notion of BiHom-generalization of Jordan superalgebras called BiHom-Jordan superalgebras in which, we investigate their representation and associated dual representation theory. We also introduce the notion of…

In this paper, we introduced the notion of Hom-Lie antialgebras. The representations and cohomology theory of Hom-Lie antialgebras are investigated. We prove that the equivalent classes of abelian extensions of Hom-Lie antialgebras are in…

We introduce a notion of left-symmetric Rinehart algebras, which is a generalization of a left-symmetric algebras. The left multiplication gives rise to a representation of the corresponding sub-adjacent Lie-Rinehart algebra. We construct…

In this paper, we give a new series of coboundary operators of Hom-Lie algebras. And prove that cohomology groups with respect to coboundary operators are isomorphic. Then, we revisit representations of Hom-Lie algebras, and generalize the…

In this paper, we introduce the representation theory of $\delta$-Hom-Jordan Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop the cohomology theory of Hom-Lie conformal superalgebras and…

The main purpose of this paper is to provide a second cohomology group of a (metric) Hom-Jacobi algebra with coefficients in a given representation. Moreover, we show that second cohomology group classifies abelian extensions of a (metric)…

It shown that the supercommutator superalgebra of a right alternative superalgebra is a Bol superalgebra. Hom-Bol superalgebras are defined and it is shown that they are closed under even self-morphisms. Any Bol superalgebra along with any…

It is shown that every multiplicative right Hom-alternative algebra is both Hom-power associative and Hom-Jordan admissible. Multiplicative right Hom-alternative algebras admit Albert-type decompositions with respect to idempotents.…

First we use a new approach to give a graded Lie algebra whose Maurer-Cartan elements characterize pre-Lie algebra structures. Then using this graded Lie bracket we define the notion of a Nijenhuis operator on a pre-Lie algebra which…

The notions of transposed Hom-Poisson and Hom-pre-Lie Poisson algebras are introduced. Their bimodules and matched pairs are defined and the relevant properties and theorems are given. The notion of Manin triple of transposed Hom-Poisson…