Super-biderivations and linear super-commuting maps on the twisted N = 2 superconformal algebra

Abstract

In this paper, we will first determine all the super-skewsymmetric super-biderivations of the twisted [Formula: see text] superconformal algebra [Formula: see text], and prove that every super-skewsymmetric super-biderivation of the twisted [Formula: see text] superconformal algebra [Formula: see text] is inner. Then, we will show that all the linear super-commuting maps on the twisted [Formula: see text] superconformal algebra [Formula: see text] are standard.

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.…”

“…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. The results in these papers [16,7,18,17,5] hold for certain superalgebras by using the approach depending on the certain superalgebras, respectively.…”

“…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.…”