Graded q-pseudo-differential Operators and Supersymmetric Algebras

TL;DR

This paper introduces a supersymmetric extension of the sine algebra and quantum algebra U_{t}(sl(2)), utilizing graded q-pseudo-differential operators with fermionic algebra to develop new supersymmetric algebraic structures.

Contribution

It provides a novel supersymmetric generalization of sine and quantum algebras using graded q-pseudo-differential operators, extending the algebraic framework to supersymmetric cases.

Findings

Supersymmetric extension of sine algebra achieved.

Construction of quantum superalgebra U_{t}(sl(2/1))

Framework for supersymmetric algebraic structures using graded operators

Abstract

We give a supersymmetric generalization of the sine algebra and the quantum algebra $U_{t}(sl(2))$. Making use of the $q$-pseudo-differential operators graded with a fermionic algebra, we obtain a supersymmetric extension of sine algebra. With this scheme we also get a quantum superalgebra $U_{t}(sl(2/1)$.