Super-biderivations of classical simple Lie superalgebras

Super-biderivations of the contact Lie superalgebra K(m,n;t¯)

“…Moreover, the authors gave the notion of the skew-symmetric superbiderivation in [11]. So the results about the skew-symmetric super-biderivation of Lie superalgebras arise in [11][12][13].…”

Super-biderivations and linear super-commuting maps on the Lie superalgebras

“…An interest in studying super-biderivations and super-commuting maps on superalgebras has grown more recently [16,18,7,17,5]. Xia, Wang and Han [16] proved that any superskewsymmetric super-biderivation of Super-Virasoro Algebras is inner and obtained the form of every linear super-commuting map.…”

“…Xia, Wang and Han [16] proved that any superskewsymmetric super-biderivation of Super-Virasoro Algebras is inner and obtained the form of every linear super-commuting map. Yuan and Tang [18] characterized super-biderivations of classical simple Lie superalgebras over the complex field C and proved that all superbiderivations of classical simple Lie superalgebras are inner super-biderivations. Fan and Dai [7] proved that all super-biderivations on the centerless super-Virasoro algebras are inner super-biderivations and studied the linear super-commuting maps on the centerless super-Virasoro algebras.…”

“…Cheng and Sun [5] proved that every super-skewsymmetric super-biderivation of the twisted N = 2 superconformal algebra is inner. The results in these papers [16,7,18,17,5] hold for certain superalgebras by using the approach depending on the certain superalgebras, respectively. In this paper, our results hold for the general Lie superalgebras satisfying certain assumptions.…”

Super-biderivations of Cartan type Lie superalgebras

“…In [17], the authors proved that any superskewsymmetric super-biderivation of super-Virasoro algebras was inner. In [18], the authors proved that all super-biderivations of classical simple Lie superalgebras were inner superbiderivations and finded a class of a non-inner and non-skewsymmetric super-biderivations of general linear Lie superalgebra. In [10], the authors determined all the biderivations of W (2, 2) and found that there existed non-inner biderivations.…”