Related papers: Twisted Rota-Baxter family operators on Hom-associ…
A LieYRep pair consists of a Lie-Yamaguti algebra and its representation. In this paper, we establish the cohomology theory of LieYRep pairs and characterize their linear deformations by the second cohomology group. Then we introduce the…
In this paper, first we give the cohomologies of an $n$-Hom-Lie algebra and introduce the notion of a derivation of an $n$-Hom-Lie algebra. We show that a derivation of an $n$-Hom-Lie algebra is a $1$-cocycle with the coefficient in the…
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…
The purpose of this paper is to define cohomology structures on Hom-associative algebras and Hom-Lie algebras. The first and second coboundary maps were introduced by Makhlouf and Silvestrov in the study of one-parameter formal deformations…
We give a broad study of representation and module theory of Rota-Baxter algebras. Regular-singular decompositions of Rota-Baxter algebras and Rota-Baxter modules are obtained under the condition of quasi-idempotency. Representations of an…
Our primary aim in this paper is to introduce and study the cohomology of a Nijenhuis operator and of a Nijenhuis algebra. Our cohomology of a Nijenhuis algebra controls the simultaneous deformations of the underlying associative structure…
In this paper, we study a new kind of vertex operator algebra related to the twisted Heisenberg-Virasoro algebra, which we call the twisted Heisenberg-Virasoro vertex operator algebra, and its modules. Specifically, we present some results…
We find connection between relative Rota--Baxter operators and usual Rota--Baxter operators. We prove that any relative Rota--Baxter operator on a group $H$ with respect to $(G, \Psi)$ defines a Rota--Baxter operator on the semi-direct…
(Tri)dendriform algebras, Rota-Baxter operators, and closely related NS-algebras have a number of dominant applications in physics, especially in quantum field theory. Proceeding from the recent study relating these structures, this paper…
The notion of matching Rota-Baxter algebras was recently introduced by Gao, Guo and Zhang [{\em J. Algebra} 552 (2020) 134-170] motivated by the study of algebraic renormalization of regularity structures. The concept of matching…
A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. In this paper, we define a cup product on the cohomology of a hom-associative algebra. We show that the cup product together with the degree…
A Rota-Baxter Lie algebra $\mathfrak{g}_T$ is a Lie algebra $\mathfrak{g}$ equipped with a Rota-Baxter operator $T : \mathfrak{g} \rightarrow \mathfrak{g}$. In this paper, we consider non-abelian extensions of a Rota-Baxter Lie algebra…
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…
In this paper, we study hom-Lie superalgebras. We give the definition of hom-Nijienhuis operators of regualr hom-Lie superalgebras and show that the deformation generated by a hom-Nijienhuis operator is trivial. Moreover, we introduce the…
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 introduce the notions of relative Rota-Baxter operators of weight $1$ on Lie-Yamaguti algebras, and post-\LYA s, which is an underlying algebraic structure of relative Rota-Baxter operators of weight $1$. We give the…
Bihom-associative algebras have been recently introduced in the study of group hom-categories. In this paper, we introduce a Hochschild type cohomology for bihom-associative algebras with suitable coefficients. The underlying cochain…
This paper is devoted to studying deformation, cohomology theory of Rota-Baxter pre-Lie algebras of arbitrary weights. First we give the notion of a new representation of a Rota-Baxter pre-Lie algebra of arbitrary weight and define the…
The notion of embedding tensors and the associated tensor hierarchies form an effective tool for the construction of supergravity and higher gauge theories. Embedding tensors and related structures are extensively studied also in the…
In this paper, we introduce the notion of modified Rota-Baxter operators of non-zero weight on $3$-Lie algebras and provide some examples. Next, we give various constructions of modified Rota-Baxter operators of non-zero weight according to…