Twisted relative Rota-Baxter operators on Leibniz algebras and NS-Leibniz algebras

Abstract

In this paper, we introduce twisted relative Rota-Baxter operators on a Leibniz algebra as a generalization of twisted Poisson structures. We define the cohomology of a twisted relative Rota-Baxter operator K as the Loday-Pirashvili cohomology of a certain Leibniz algebra induced by K with coefficients in a suitable representation. Then we consider formal deformations of twisted relative Rota-Baxter operators from cohomological points of view. Finally, we introduce and study NS-Leibniz algebras as the underlying structure of twisted relative Rota-Baxter operators.

Representations and cohomolgies of Rota-Baxter 3-Lie algebras

“…In the same direction, Das gave cohomology and deformation theories of associative Rota-Baxter operators of weight 0 in [11,16] and relative Rota-Baxter operators with any weight [14]. The cohomology and deformation of twisted Rota-Baxter operators were considered in [12,13]. Another breakthrough gained by Wang and Zhou in [37] is cohomology and homotopy theories of Rota-Baxter algebras with any weight.…”

Generalized Reynolds Operators on Lie-Yamaguti Algebras

“…The cohomology and deformations of twisted Rota-Baxter operators on associative algebras was studied by Das [6]. Twisted Rota-Baxter operators have been introduced and widely studied for other algebraic structures such as Lie algebras [7], Leibniz algebras [8] and 3-Lie algebras [9,10].…”

Deformations and homotopy theory of Rota-Baxter algebras of any weight

“…Later Das and Misha also determined the L ∞ -structures underlying the cohomology theory for Rota-Baxter associative algebras of weight zero [17]. There are some other related work [62,63,11,12,13,15,16]. These work all concern Rota-Baxter operators of weight zero.…”