Related papers: Noncommutative Poisson bialgebras
We establish a bialgebra theory for differential algebras, called differential antisymmetric infinitesimal (ASI) bialgebras by generalizing the study of ASI bialgebras to the context of differential algebras, in which the derivations play…
In this paper, the notions of quasi-triangular and factorizable dual pre-Poisson bialgebras are introduced. A factorizable dual pre-Poisson bialgebra induces a factorization of the underlying dual pre-Poisson algebra, and the double of any…
In this paper, we construct a bialgebra theory for associative conformal algebras, namely antisymmetric infinitesimal conformal bialgebras. On the one hand, it is an attempt to give conformal structures for antisymmetric infinitesimal…
We study possible connections between Rota-Baxter operators of non-zero weight and non-skew-symmetric solutions of the classical Yang-Baxter equation on finite-dimensional quadratic Lie algebras. The particular attention is made to the case…
In this paper, I will show that, if a Lie algebra $\G$ acts on a manifold $P$, any solution of the classical Yang-Baxter equation on $\G$ gives arise to a Poisson tensor on $P$ and a torsion-free and flat contravariant connection (with…
We introduce a novel approach that employs techniques from noncommutative Poisson geometry to comprehend the algebra of invariants of two $n\times n$ matrices. We entirely solve the open problem of computing the algebra of invariants of two…
We consider non-ultra local linear Poisson algebras on a continuous line . Suitable combinations of representations of these algebras yield representations of novel generalized linear Poisson algebras or "boundary" extensions. They are…
Let $L$ be a simple anti-commutative algebra. In this paper we prove that a non skew-symmetric solution of the classical Yang-Baxter equation on $L$ with $L$-invariant symmetric part induces on $L$ a Rota-Baxter operator of a non-zero…
The paper is devoted to the Poisson brackets compatible with multiplication in associative algebras. These brackets are shown to be quadratic and their relations with the classical Yang--Baxter equation are revealed. The paper also contains…
This paper studies two types of 3-Lie bialgebras whose compatibility conditions between the multiplication and comultiplication are given by local cocycles and double constructions respectively, and are therefore called the local cocycle…
In the paper, we introduce the notion of a Rota-Baxter operator of a non-scalar weight. As a motivation, we show that there is a natural connection between Rota-Baxter operators of this type and structures of quasitriangular Lie bialgebras…
Rota-Baxter operators and bialgebras are closely connected in several applications, such as the Connes-Kreimer renormalization framework and the operator approach to the classical Yang-Baxter equation. The concept of a Rota-Baxter system…
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…
A Hom-type generalization of non-commutative Poisson algebras, called non-commutative Hom-Poisson algebras, are studied. They are closed under twisting by suitable self-maps. Hom-Poisson algebras, in which the Hom-associative product is…
We give relations between dynamical Poisson groupoids, classical dynamical Yang--Baxter equations and Lie quasi-bialgebras. We show that there is a correspondance between the class of bidynamical Lie quasi-bialgebras and the class of…
Conformal classical Yang-Baxter equation and $S$-equation naturally appear in the study of Lie conformal bialgebras and left-symmetric conformal bialgebras. In this paper, they are interpreted in terms of a kind of operators, namely,…
We introduce a notion of a para-K\"{a}hler strict Lie 2-algebra, which can be viewed as a categorification of a para-K\"{a}hler Lie algebra. In order to study para-K\"{a}hler strict Lie 2-algebra in terms of strict pre-Lie 2-algebras, we…
In this paper, we derive pre-anti-flexible algebras structures in term of zero weight's Rota-Baxter operators defined on anti-flexible algebras, view pre-anti-flexible algebras as a splitting of anti-flexible algebras, introduce the notion…
We introduce a notion of noncommutative Poisson-Nijenhuis structure on the path algebra of a quiver. In particular, we focus on the case when the Poisson bracket arises from a noncommutative symplectic form. The formalism is then applied to…
The aim of this paper is twofold. In the first part, we define the cohomology of a Nijenhuis Lie algebra with coefficients in a suitable representation. Our cohomology of a Nijenhuis Lie algebra governs the simultaneous deformations of the…