Super-biderivations of Lie superalgebras

Abstract

In this paper we attempt to investigate the super-biderivations of Lie superalgebras. Furthermore, we prove that all super-biderivations on the centerless super-Virasoro algebras are inner super-biderivations. Finally, we study the linear super commuting maps on the centerless super-Virasoro algebras.

Biderivations of finite-dimensional complex simple Lie algebras

“…also forget the assumption of super-skewsymmetric [19]. Besides that, about this class of problems on biderivation of Lie (super-)algebra, f is supposed to be (super-)skewsymmetric and applied the conclusion of Assumption 1.2 [8,10,13,16,18]. In this paper, the assumption of skewsymmetric will not be applied.…”

Biderivations and Commutative Post-Lie Algebra Structures on the Lie Algebra $\mathcal{W}(a,b)$

“…The notion of biderivations was introduced to Lie algebras in [21]. Later super-biderivations on some super-algebras was introduced in [7,22]. For the last few years many authors computed only skew-symmetric biderivations of some Lie (super)algebras due to their close relation to commuting maps, see [6,7,10,[20][21][22].…”

Super-biderivations and Linear Super-commuting Maps on the N 2 Superconformal Algebra

“…For basic concepts and usual notations on Lie superalgebras, we refer to [7] for details. Now, we first give the concept of super-commuting map on a Lie superalgebra, which has been given in [9] and [4], independently.…”

“…Similarly, the concept of super-biderivation plays the same roles in associative superalgebras and Lie superalgebras when studying the linear super-commuting maps. As a generalization of biderivations of Lie algebras and a parallel concept of superbiderivation of an associative superalgebra, the concept of super-biderivation of a Lie superalgebra was introduced in [9] and [4] indepently as follows.…”