Curtright-Zachos Supersymmetric Deformations of the Virasoro algebra in Quantum Superspace and Bloch Electron Systems

TL;DR

This paper develops supersymmetric deformations of the Virasoro algebra within quantum superspace, applying the framework to Bloch electron systems under magnetic effects, revealing structural parallels between algebraic and physical models.

Contribution

It introduces supersymmetric extensions of the Hom-Lie deformation of the Virasoro algebra in quantum superspace, applied to Bloch electron systems with Zeeman effects.

Findings

Constructed supersymmetric deformations in quantum superspace.

Linked algebraic structures to Bloch electron systems.

Revealed structural parallels between algebra and physical systems.

Abstract

We introduce supersymmetric extensions of the Hom-Lie deformation of the Virasoro algebra, as realized in the GL(1,1) quantum superspace, for Bloch electron systems under Zeeman effects. The construction is achieved by defining generators through magnetic translations and spin matrix bases, specifically for the N=1 and N=2 supersymmetric deformed algebras. This approach reveals a structural parallel between the deformed algebra in quantum superspace and its manifestation in Bloch electron systems.