Related papers: Rota-Baxter systems and skew trusses
Braces were introduced by Rump to study non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation. We generalize Rump's braces to the non-commutative setting and use this new structure to study not necessarily involutive…
In this paper, we introduce the notion of a relative Rota-Baxter operator of weight $\lambda$ on a Lie triple system with respect to an action on another Lie triple system, which can be characterized by the graph of their semidirect…
In this paper we discuss and characterize several set-theoretic solutions of the Yang-Baxter equation obtained using skew lattices, an algebraic structure that has not yet been related to the Yang-Baxter equation. Such solutions are…
We introduce a new point of view to present classical notions related to set-theoretic solutions of the Yang-Baxter equation: left skew braces, dirings, left skew rings. The idea is to replace the single multiplication on a left near-ring…
The main aim of this paper is to provide set-theoretical solutions of the Yang-Baxter equation that are not necessarily bijective, among these new idempotent ones. In the specific, we draw on both to the classical theory of inverse…
M. Goncharov introduced and studied a Rota--Baxter operator on a cocommutative Hopf algebra. In the present paper we define relative Rota--Baxter operators on an arbitrary Hopf algebra. A particular case of this definition is Goncharov's…
This paper introduces the notion of Rota-Baxter $C^{\ast}$-algebras. Here a Rota-Baxter $C^{\ast}$-algebra is a $C^{\ast}$-algebra with a Rota-Baxter operator. Symmetric Rota-Baxter operators, as special cases of Rota-Baxter operators on…
As Hopf truss analogues of Rota-Baxter Hopf algebras, the notion of Rota-Baxter systems of Hopf algebras is proposed. We study the relatiohship between Rota-Baxter systems of Hopf algebras and Rota-Baxter Hopf algebras, show that there is a…
In this paper, we first introduce twisted Rota-Baxter families on Lie-Yamaguti algebras indexed by a commutative semigroup $\Omega$. Then, we study NS-Lie-Yamaguti family algebras as the underlying structures of twisted Rota-Baxter…
In this paper, we introduce the notion of Rota-Baxter Lie $2$-algebras, which is a categorification of Rota-Baxter Lie algebras. We prove that the category of Rota-Baxter Lie $2$-algebras and the category of $2$-term Rota-Baxter…
The notion of post-groups was introduced by Bai, Guo and the first two authors recently, which are the global objects corresponding to post-Lie algebras, equivalent to skew-left braces, and can be used to construct set-theoretical solutions…
In the 1990s, Drinfel'd proposed the study of set-theoretical solutions to the quantum Yang-Baxter equation, initiating a line of research that has since garnered substantial attention and led to notable developments in algebra,…
In this paper, we introduce relative Rota-Baxter systems on Leibniz algebras and give some characterizations and new constructions. Then we construct a graded Lie algebra whose Maurer-Cartan elements are relative Rota-Baxter systems. This…
A relative Rota-Baxter algebra is a triple $(A, M, T)$ consisting of an algebra $A$, an $A$-bimodule $M$, and a relative Rota-Baxter operator $T$. Using Voronov's derived bracket and a recent work of Lazarev et al., we construct an…
As a fundamental and ubiquitous combinatorial notion, species has attracted sustained interest, generalizing from set-theoretical combinatorial to algebraic combinatorial and beyond. The Rota-Baxter algebra is one of the algebraic…
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…
Relative Rota-Baxter groups are generalizations of Rota-Baxter groups and share a close connection with skew left braces. These structures are well-known for offering bijective non-degenerate set-theoretical solutions to the Yang-Baxter…
In this paper, we establish a local Lie theory for relative Rota-Baxter operators of weight $1$. First we recall the category of relative Rota-Baxter operators of weight $1$ on Lie algebras and construct a cohomology theory for them. We use…
The notions of a post-group and a pre-group are introduced as a unification and enrichment of several group structures appearing in diverse areas from numerical integration to the Yang-Baxter equation. First the Butcher group from numerical…
We investigate a new algebraic structure which always gives rise to a set-theoretic solution of the Yang-Baxter equation. Specifically, a weak (left) brace is a non-empty set $S$ endowed with two binary operations $+$ and $\circ$ such that…