Related papers: Deformations of associative Rota-Baxter operators
In this paper we construct a graded Lie algebra on the space of cochains on a $\mathbbZ_2$-graded vector space that are skew-symmetric in the odd variables. The Lie bracket is obtained from the classical Gerstenhaber bracket by (partial)…
Rota-Baxter operators are an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota-Baxter operators and integrals in the case of the polynomial algebra $\mathbf{k}[x]$. We consider…
A Rota-Baxter operator of weight $\lambda$ is an abstraction of both the integral operator (when $\lambda=0$) and the summation operator (when $\lambda=1$). We similarly define a differential operator of weight $\lambda$ that includes both…
In this paper, we study relative Rota-Baxter operators of weight $0$ on groups and give various examples. In particular, we propose different approaches to study Rota-Baxter operators of weight $0$ on groups and Lie groups. We establish…
In a classic paper, Gerstenhaber showed that first order deformations of an associative k-algebra A are controlled by the second Hochschild cohomology group of A. More generally, any n-parameter first order deformation of A gives, due to…
The aim of this paper is to provide a cohomology of $n$-Hom-Lie color algebras governing one parameter formal deformations. Then, we study formal deformations of a $n$-Hom-Lie color algebra and introduce the notion of Nijenhuis operator on…
In this paper, we first introduce the notion of a (relative) averaging operator of any nonzero weight $\lambda$. We show that such operators are intimately related to triassociative algebras introduced by Loday and Ronco. Next, we construct…
Rota-Baxter operators present a natural generalisation of integration by parts formula for the integral operator. In 2015, Zheng, Guo, and Rosenkranz conjectured that every injective Rota-Baxter operator of weight zero on the polynomial…
In this paper, we begin a systematic study of modified Rota-Baxter algebras, as an associative analogue of the modified classical Yang-Baxter equation. We construct free commutative modified Rota-Baxter algebras by a variation of the…
Unifying various generalizations of the important notions of Reynolds operators, the relative cocycle weighted Reynolds operators are studied. Here cocycle weighted means the weight of the operators is given by a 2-cocycle rather than by a…
We develop a deformation theory for finite-dimensional left-symmetric color algebras, which can be used to construct new algebraic structures and interpret left-symmetric color cohomology spaces of lower degrees. We explore equivalence…
We present an orthogonal basis of gauge invariant operators constructed from some complex matrices for the free matrix field, where operators are expressed with the help of Brauer algebra. This is a generalisation of our previous work for a…
A ternary Nambu-Poisson algebra (which we call a Nambu-Poisson algebra in the paper) is the underlying algebraic structure of Nambu-Poisson manifolds of order $3$ that appeared in the generalized Hamiltonian mechanics. First, we consider…
We introduce an equivariant version of Hochschild cohomology as the deformation cohomology to study equivariant deformations of associative algebras equipped with finite group actions.
We determine the \emph{$L_\infty$-algebra} that controls deformations of a relative Rota-Baxter Lie algebra and show that it is an extension of the dg Lie algebra controlling deformations of the underlying LieRep pair by the dg Lie algebra…
This paper investigates Rota-Baxter systems in the sense of Brzezi\'nski from the perspective of operad theory. The minimal model of the Rota-Baxter system operad is constructed, equivalently a concrete construction of its Koszul dual…
We propose a definition of differential operators of an associative algebra $A$ in the spirit of Hochschild cohomology. Specifically we define $D(A)$ as the zero cohomology of a certain bicomplex formed by Hom-spaces…
The goal of the present paper is to investigate representations and cohomologies of Rota-Baxter 3-Lie algebras with any weight. We introduce representations, matched pairs and Manin triples of Rota-Baxter 3-Lie algebras. Furthermore, we…
In this paper, first we construct two subcategories (using symmetric representations and antisymmetric representations) of the category of relative Rota-Baxter operators on Leibniz algebras, and establish the relations with the categories…
Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebra and root vectors and which make it possible to construct representations by operators acting…