Curtright-Zachos supersymmetric deformations of the Virasoro algebra in quantum superspace and Bloch electron 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.