BiHom-pre-Lie algebras, BiHom-Leibniz algebras and Rota–Baxter operators on BiHom-Lie algebras
-
Ling Liu
,
Claudia Menini
Abstract
We contribute to the study of Rota–Baxter operators on types of algebras other than associative and Lie algebras. If A is an algebra of a certain type and R is a Rota–Baxter operator on A, one can define a new multiplication on A by means of R and the previous multiplication and ask under what circumstances the new algebra is of the same type as A. Our first main result deals with such a situation in the case of BiHom-Lie algebras. Our second main result is a BiHom analogue of Aguiar’s theorem that shows how to obtain a pre-Lie algebra from a Rota–Baxter operator of weight zero on a Lie algebra. The BiHom analogue does not work for BiHom-Lie algebras, but for a new concept we introduce here, called left BiHom-Lie algebra, at which we arrived by defining first the BiHom version of Leibniz algebras.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11801515
Award Identifier / Grant number: 11601486
Funding statement: This paper was written while Ling Liu was visiting the Institute of Mathematics of the Romanian Academy (IMAR), supported by the NSF of China (Grant Nos. 11801515, 11601486). Claudia Menini was a member of the National Group for Algebraic and Geometric Structures, and their Applications (GNSAGA-INdAM). This paper was partially supported by MIUR within the National Research Project PRIN (Grant No. 2017/201789N23_5002).
Acknowledgements
Ling Liu would like to thank IMAR for hospitality.
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Articles in the same Issue
- Frontmatter
- Ulam type stability for non-instantaneous impulsive Caputo fractional differential equations with finite state dependent delay
- m-potent commutators involving skew derivations and multilinear polynomials
- On some higher order equations admitting meromorphic solutions in a given domain
- Mixed- and crack-type dynamical problems of electro-magneto-elasticity theory
- Regular Hom-algebras admitting a multiplicative basis
- The uniform convergence of a double sequence of functions at a point and Korovkin-type approximation theorems
- On the generalized nonmeasurability of Vitali sets and Bernstein sets
- BiHom-pre-Lie algebras, BiHom-Leibniz algebras and Rota–Baxter operators on BiHom-Lie algebras
- An extension of the Muckenhoupt–Wheeden theorem to generalized weighted Morrey spaces
- Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions
- Weighted higher order exponential type inequalities in metric spaces and applications
- Admissible Galois Structures on the categories dual to some varieties of universal algebras
Articles in the same Issue
- Frontmatter
- Ulam type stability for non-instantaneous impulsive Caputo fractional differential equations with finite state dependent delay
- m-potent commutators involving skew derivations and multilinear polynomials
- On some higher order equations admitting meromorphic solutions in a given domain
- Mixed- and crack-type dynamical problems of electro-magneto-elasticity theory
- Regular Hom-algebras admitting a multiplicative basis
- The uniform convergence of a double sequence of functions at a point and Korovkin-type approximation theorems
- On the generalized nonmeasurability of Vitali sets and Bernstein sets
- BiHom-pre-Lie algebras, BiHom-Leibniz algebras and Rota–Baxter operators on BiHom-Lie algebras
- An extension of the Muckenhoupt–Wheeden theorem to generalized weighted Morrey spaces
- Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions
- Weighted higher order exponential type inequalities in metric spaces and applications
- Admissible Galois Structures on the categories dual to some varieties of universal algebras
