相关论文: Extensions of (metric) Hom-Jacobi-Jordan algebras

This paper develops a cohomology theory for Hom-Jacobi-Jordan algebras using and applies it to classify non-abelian extensions. The main result establishes that equivalence classes of split extensions of a Hom-Jacobi-Jordan algebra $J$ by…

The main purpose of this paper is to provide a full cohomology of a Hom-pre-Lie algebra with coefficients in a given representation. This new type of cohomology exploit strongly the Hom-type structure and fits perfectly with simultaneous…

In this paper, we first introduce the concept and representations of modified $\lambda$-differential Lie-Yamaguti algebras. We then establish the cohomology of a modified $\lambda$-differential Lie-Yamaguti algebra with coefficients in a…

In this paper, we define and develop a cohomology and deformation theories of Jacobi-Jordan algebras. We construct a cohomology based on two operators, called zigzag cohomology, and detail the low degree cohomology spaces. We describe the…

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…

In this paper, first we give the notion of a representation of a relative Rota-Baxter Lie algebra and introduce the cohomologies of a relative Rota-Baxter Lie algebra with coefficients in a representation. Then we classify abelian…

The representation and cohomology theory of Hom-Lie-Yamaguti algebras is introduced. As an application, we study deformation and extension of Hom-Lie-Yamaguti algebras. It proved that a 1-parameter infinitesimal deformation of a…

In this paper, first we introduce the concept of modified Rota-Baxter Lie-Yamaguti algebras. Then the cohomology of a modified Rota-Baxter Lie-Yamaguti algebra with coefficients in a suitable representation is established. As applications,…

In this paper, we introduce the concept of crossed module for Hom-Leibniz-Rinehart algebras. We study the cohomology and extension theory of Hom-Leibniz-Rinehart algebras. It is proved that there is one-to-one correspondence between…

We introduce hom-Lie-Rinehart algebras as an algebraic analogue of hom-Lie algebroids, and systematically describe a cohomology complex by considering coefficient modules. We define the notion of extensions for hom-Lie-Rinehart algebras. In…

The purpose of this paper is to define the representation and the cohomology of Hom-Lie superalgebras. Moreover we study Central extensions and provide as application the computations of the derivations and second cohomology group of…

We introduce the concept of Hom-associative algebra structures in Loday-Pirashvili category.The cohomology theory of Hom-associative algebras in this category is studied.Some applications on deformation and abelian extension theory are…

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, 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…

We define cohomology of associative H-pseudoalgebras, and we show that it describes module extensions, abelian pseudoalgebra extensions, and pseudoalgebra first order deformations. We describe in details the same results for the special…

The representation and the cohomology theory of associative 2-algebras are developed. We study the deformations and abelian extensions of associative 2-algebras in details.

For a class of pointed Hopf algebras including the quantized enveloping algebras, we discuss cleft extensions, cocycle deformations and the second cohomology. We present such a non-standard method of computing the abelian second cohomology…

In this article, we introduce a new cohomology theory associated to a Lie 2-algebras. This cohomology theory is shown to extend the classical cohomology theory of Lie algebras; in particular, we show that the second cohomology group…

The aim of this paper is to introduce 3-Hom-$\rho$-Lie algebra structures generalizing the algebras of 3-Hom-Lie algebra. Also, we investigate the representations and deformations theory of this type of Hom-Lie algebras. Moreover, we…

In this paper, we define the cohomology of a modified Rota-Baxter Leibniz algebra with coefficients in a suitable representation. As applications of our cohomology, we study formal one-parameter deformations and abelian extensions of…