Super-biderivations of Cartan type Lie superalgebras

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.…”

“…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. Yuan, Chen and Cao [17] characterized the super-biderivations of Cartan type Lie superalgebras over the complex field C and proved that all super-biderivations of Cartan type simple Lie superalgebras are inner super-biderivations. Cheng and Sun [5] proved that every super-skewsymmetric super-biderivation of the twisted N = 2 superconformal algebra is inner.…”

“…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.…”