Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Rota-Baxter 3-Lie algebras
View through CrossRef
In this paper, we introduce the concepts of a Rota-Baxter operator and differential operator with weights on an n-algebra. We then focus on Rota-Baxter 3-Lie algebras and show that they can be derived from Rota-Baxter Lie algebras and pre-Lie algebras and from Rota-Baxter commutative associative algebras with derivations. We also establish the inheritance property of Rota-Baxter 3-Lie algebras.
Title: Rota-Baxter 3-Lie algebras
Description:
In this paper, we introduce the concepts of a Rota-Baxter operator and differential operator with weights on an n-algebra.
We then focus on Rota-Baxter 3-Lie algebras and show that they can be derived from Rota-Baxter Lie algebras and pre-Lie algebras and from Rota-Baxter commutative associative algebras with derivations.
We also establish the inheritance property of Rota-Baxter 3-Lie algebras.
Related Results
Deformation Maps of Quasi-Twilled Lie Algebras
Deformation Maps of Quasi-Twilled Lie Algebras
In this paper, we provide a unified approach to study the cohomology theories and deformation theories of various types of operators in the category of Lie algebras, including modi...
The L∞-deformations of associative Rota–Baxter algebras and homotopy Rota–Baxter operators
The L∞-deformations of associative Rota–Baxter algebras and homotopy Rota–Baxter operators
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 recen...
Quasi-pre-Lie bialgebras and twisting of pre-Lie algebras
Quasi-pre-Lie bialgebras and twisting of pre-Lie algebras
Given a (quasi-)twilled pre-Lie algebra, we first construct a differential graded Lie algebra ([Formula: see text]-algebra). Then we study the twisting theory of (quasi-)twilled pr...
Averaging pre-Lie bialgebras and the related admissible classical Yang-Baxter equations
Averaging pre-Lie bialgebras and the related admissible classical Yang-Baxter equations
In this paper, we initiate the representation theory for averaging pre-Lie algebras, and establish the intrinsic equivalence among matched pairs, Manin triples, and bialgebra struc...
Deformations and Cohomologies of Relative Rota-Baxter Operators on Lie Algebroids and Koszul-Vinberg Structures
Deformations and Cohomologies of Relative Rota-Baxter Operators on Lie Algebroids and Koszul-Vinberg Structures
Given a Lie algebroid with a representation, we construct a graded Lie algebra whose Maurer-Cartan elements characterize relative Rota-Baxter operators on Lie algebroids. We give t...
Hopf group braces, post-Hopf group algebras and Rota–Baxter operators on Hopf group algebras
Hopf group braces, post-Hopf group algebras and Rota–Baxter operators on Hopf group algebras
In this paper, we introduce the notions of Hopf group braces, post-Hopf group algebras, and Rota–Baxter Hopf group algebras as important generalizations of Hopf braces, post-Hopf a...
Differential graded vertex Lie algebras
Differential graded vertex Lie algebras
This is the continuation of the study of differential graded (dg) vertex algebras defined in our previous paper [Caradot et al., “Differential graded vertex operator algebras and t...
Embedding of dendriform algebras into Rota-Baxter algebras
Embedding of dendriform algebras into Rota-Baxter algebras
Abstract
Following a recent work [Bai C., Bellier O., Guo L., Ni X., Splitting of operations, Manin products, and Rota-Baxter operators, Int. Math. Res. Not. IMRN (i...