2023/08/15 by Yuan, Lamei, Liu, Jiefeng · 3 citations
#16D70 #17A30 #17B55 #FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2308.07596
Based on Nijenhuis-Richardson bracket and bidegree on the cohomology complex for a Lie conformal algebra, we develop a twisting theory of Lie conformal algebras. By using derived bracket constructions, we construct L_∞-algebras from (quasi-)twilled Lie conformal algebras. And we show that the result of the twisting by a ℂ[∂]-module homomorphism on a (quasi-)twilled Lie conformal algebra is also a (quasi-)twilled Lie conformal algebra if and only if the ℂ[∂]-module homomorphism is a Maurer-Cartan element of the L_∞-algebra. In particular, we show that relative Rota-Baxter type operators on Lie conformal algebras are Maurer-Cartan elements. Besides, we propose a new algebraic structure, called NS-Lie conformal algebras, that is closely related to twisted relative Rota-Baxter operators and Nijenhuis operators on Lie conformal algebras. As an application of twisting theory, we give the cohomology of twisted relative Rota-Baxter operators and study their deformations.