Loop Virasoro Lie conformal superalgebra

Abstract

The loop super-Virasoro conformal superalgebra cls associated with the loop super-Virasoro algebra is constructed in the present paper. The conformal superderivation algebra of cls is completely determined, which is shown to consist of inner superderivations. And nontrivial free and free Z-graded cls-modules of rank two are classified. We also give a classification of irreducible free cls-modules of rank two and all irreducible submodules of each free Z-graded cls-module of rank two.In this section, we recall some notions related to Lie conformal superalgebras and conformal modules from [8,12,13].

Conformal Super-Biderivations on Lie Conformal Superalgebras

“…Finite simple Lie conformal superalgebras were classified by Fattori and Kac in [2], and their representation theories were developed in [3][4][5]. Moreover, some infinite Lie conformal superalgebras were also studied, such as loop super-Virasoro Lie conformal superalgebra [6] and Lie conformal superalgebras of Block type [7]. Other results on Lie conformal superalgebras can be seen in [8,9].…”

“…In this paper, we concentrate on the loop super-Virasoro Lie conformal superalgebra cls (see [6]), which is defined as a…”