Aspects of infinite dimensional $\ell$-super Galilean conformal algebra

TL;DR

This paper constructs and analyzes an infinite dimensional $ ell$-super Galilean conformal algebra, extending previous work for $ ell=1$, and explores its mathematical structure with potential applications in physics.

Contribution

It introduces a generalized $ ell$-super Galilean conformal algebra, providing classification, representations, and operator product expansion analysis.

Findings

Classification of central extensions

Vector field and coadjoint representations

Operator product expansion derived

Abstract

In this work we construct a infinite dimensional $\ell$-super Galilean conformal algebra, which is a generalization of the $\ell=1$ algebra found in the literature. We give a classification of central extensions, the vector field representation, the coadjoint representation and the operator product expansion of the infinite dimensional $\ell$-super Galilean conformal algebra, keeping possible applications in physics and mathematics in mind.