1. Quasi-pre-Lie bialgebras and twisting of pre-Lie algebras.
- Author
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Wang, Qi and Liu, Jiefeng
- Abstract
Given a (quasi-)twilled pre-Lie algebra, we first construct a differential graded Lie algebra (L∞-algebra). Then we study the twisting theory of (quasi-)twilled pre-Lie algebras and show that the result of the twisting by a linear map on a (quasi-)twilled pre-Lie algebra is also a (quasi-)twilled pre-Lie algebra if and only if the linear map is a solution of the Maurer–Cartan equation of the associated differential graded Lie algebra (L∞-algebra). In particular, the relative Rota–Baxter operators (twisted relative Rota–Baxter operators) on pre-Lie algebras are solutions of the Maurer–Cartan equation of the differential graded Lie algebra (L∞-algebra) associated to the certain quasi-twilled pre-Lie algebra. Finally, we use the twisting theory of (quasi-)twilled pre-Lie algebras to study quasi-pre-Lie bialgebras. Moreover, we give a construction of quasi-pre-Lie bialgebras through symplectic Lie algebras, which is parallel to that a Cartan 3-form on a semi-simple Lie algebra gives a quasi-Lie bialgebra. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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