Loop super-Virasoro Lie conformal superalgebra

TL;DR

This paper constructs the loop super-Virasoro conformal superalgebra, determines its superderivation algebra, and classifies its free and irreducible modules of rank two, advancing the understanding of its structure and representations.

Contribution

It introduces the loop super-Virasoro conformal superalgebra and classifies its superderivations and modules, providing new insights into its algebraic structure and representation theory.

Findings

Superderivation algebra consists solely of inner superderivations.

Classified nontrivial free and free $ abla$-graded modules of rank two.

Provided a complete classification of irreducible free modules of rank two.

Abstract

The loop super-Virasoro conformal superalgebra $\mathfrak{cls}$ associated with the loop super-Virasoro algebra is constructed in the present paper. The conformal superderivation algebra of $\mathfrak{cls}$ is completely determined, which is shown to consist of inner superderivations. And nontrivial free and free $\mathbb{Z}$-graded $\mathfrak{cls}$-modules of rank two are classified. We also give a classification of irreducible free $\mathfrak{cls}$-modules of rank two and all irreducible submodules of each free $\mathbb{Z}$-graded $\mathfrak{cls}$-module of rank two.