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We introduce the conception of matched pairs of $(H, beta)$-Lie algebras, construct an $(H, beta)$-Lie algebra through them. We prove that the cocycle twist of a matched pair of $(H, beta)$-Lie algebras can also be matched.
In this paper, first we introduce the notion of a twilled 3-Lie algebra, and construct an $L_infty$-algebra, whose Maurer-Cartan elements give rise to new twilled 3-Lie algebras by twisting. In particular, we recover the Lie $3$-algebra whose Maurer-
Serious difficulties arise in the construction of chains of twists for symplectic Lie algebras. Applying the canonical chains of extended twists to deform the Hopf algebras U(sp(N)) one is forced to deal only with improper chains (induced by the U(sl
We study (quasi-)twilled pre-Lie algebras and the associated $L_infty$-algebras and differential graded Lie algebras. Then we show that certain twisting transformations on (quasi-)twilled pre-Lie algbras can be characterized by the solutions of Maure
In this article we develop an approach to deformations of the Witt and Virasoro algebras based on $sigma$-derivations. We show that $sigma$-twisted Jacobi type identity holds for generators of such deformations. For the $sigma$-twisted generalization
We determine the emph{$L_infty$-algebra} that controls deformations of a relative Rota-Baxter Lie algebra and show that it is an extension of the dg Lie algebra controlling deformations of the underlying LieRep pair by the dg Lie algebra controlling