Simple Harish-Chandra modules over the super affine-Virasoro algebras

TL;DR

This paper classifies all simple Harish-Chandra modules over a complex super affine-Virasoro algebra, expanding understanding of representations in superalgebra contexts with specific algebraic structures.

Contribution

It provides a complete classification of simple Harish-Chandra modules over the super affine-Virasoro algebra, a novel result in the representation theory of superalgebras.

Findings

Complete classification of simple Harish-Chandra modules achieved.

Identification of module structures over the super affine-Virasoro algebra.

Extension of representation theory to superalgebra frameworks.

Abstract

In this paper, we classify all simple Harish-Chandra modules over the super affine-Virasoro algebra $\widehat{\mathcal{L}}=\mathcal{W}\ltimes(\mathfrak{g}\otimes \mathcal{A})\oplus \mathbb{C}C$, where $\mathcal{A}=\mathbb{C}[t^{\pm 1}]\otimes\Lambda(1)$ is the tensor superalgebra of the Laurent polynomial algebra in even variable $t$ and the Grassmann algebra in odd variable $\xi$, $\mathcal{W}$ is the Lie superalgebra of superderivations of $\mathcal{A}$, and $\mathfrak{g}$ is a finite-dimensional perfect Lie superalgebra.