Search
Search Results
-
Rota-Baxter Lie bialgebras, classical Yang-Baxter equations and special L-dendriform bialgebras
This paper extends the well-known fact that a Rota-Baxter operator of weight 0 on a Lie algebra induces a pre-Lie algebra, to the level of...
-
Rota–Baxter operators on groups
The theory of Rota–Baxter operators on rings and algebras has been developed since 1960. In 2020, the notion of Rota–Baxter operator on a group was...
-
3-pre-Leibniz Algebras, Deformations and Cohomologies of Relative Rota-Baxter Operators on 3-Leibniz Algebras
In this paper, first we introduce the notions of 3-pre-Leibniz algebras and relative Rota-Baxter operators on 3-Leibniz algebras. We show that a...
-
Bimodules over Relative Rota-Baxter Algebras and Cohomologies
A relative Rota-Baxter algebra is a generalization of a Rota-Baxter algebra. Relative Rota-Baxter algebras are closely related to dendriform...
-
Free Rota-Baxter Family Algebras and Free (tri)dendriform Family Algebras
In this paper, we first construct the free Rota-Baxter family algebra generated by some set X in terms of typed angularly X -decorated planar rooted...
-
BiHom-NS-Algebras, Twisted Rota–Baxter Operators and Generalized Nijenhuis Operators
The purpose of this paper is to introduce and study BiHom-NS-algebras, which are a generalization of NS-algebras using two homomorphisms. Moreover,...
-
Cohomology and deformations of twisted Rota–Baxter operators and NS-algebras
The aim of this paper is twofold. In the first part, we consider twisted Rota–Baxter operators on associative algebras that were introduced by Uchino...
-
Modules of Non-unital Polynomial Rota-Baxter Algebras
In this paper, we study the free commutative non-unital Rota-Baxter algebra which is the algebra of polynomials in one variable without constant term...
-
Skew braces from Rota–Baxter operators: a cohomological characterisation and some examples
Rota–Baxter operators for groups were recently introduced by Guo, Lang, and Sheng. Bardakov and Gubarev showed that with each Rota–Baxter operator,...
-
Rota–Baxter operators on involutive associative algebras
In this paper, we consider Rota–Baxter operators on involutive asso-ciative algebras. We define cohomology for Rota–Baxter operators on...
-
Monomial Rota–Baxter Operators of Nonzero Weight on F[x, y] Coming from Averaging Operators
The intensive study of Rota–Baxter operators on the polynomial algebra F [ x ] has been started with the work of Zheng et al. (Pac J Math (2) 275:481–...
-
Homothetic Rota–Baxter Systems and Dyck \(^m\) -Algebras
It is shown that generalized Rota–Baxter operators introduced in [W. A. Martinez, E. G. Reyes, M. Ronco, Int. J. Geom. Meth. Mod. Phys. 18, 2150176...
-
Hopf algebra structure on free Rota–Baxter algebras by angularly decorated rooted trees
By means of a new notion of subforests of an angularly decorated rooted forest, we give a combinatorial construction of a coproduct on the free...
-
Injective Rota–Baxter Operators of Weight Zero on F[x]
Rota–Baxter operators present a natural generalization of integration by parts formula for the integral operator. In 2015, Zheng, Guo, and Rosenkranz...
-
Rota–Baxter Operators on the Simple Jordan Superalgebra \( D_{t} \)
Up to conjugation by an automorphism, we describe the Rota–Baxter operators of weight zero or nonzero on the simple four-dimensional Jordan...
-
Post-groups, (Lie-)Butcher groups and the Yang–Baxter equation
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...
-
Burde’s series of simple pre-Lie algebras
We describe automorphisms, derivations, and Rota–Baxter operators on the series of simple pre-Lie algebras found by D. Burde in 1998.
-
Integral Operators on Lattices
As an abstraction and generalization of the integral operator in analysis, integral operators (known as Rota-Baxter operators of weight zero) on...