Semi-Hopf Algebra and Supersymmetry

TL;DR

This paper introduces semi-Hopf algebras as a generalization of Hopf algebras and constructs supersymmetry algebras with quantum gauge groups, providing explicit N=1 and N=2 supersymmetric Lagrangians.

Contribution

It defines semi-Hopf algebras and demonstrates their use in constructing supersymmetry algebras with quantum gauge groups, extending the mathematical framework of supersymmetry.

Findings

Construction of supersymmetry algebra via semi-Hopf algebra

Explicit N=1 and N=2 supersymmetric Lagrangians

Integration of quantum gauge groups into supersymmetry

Abstract

We define a semi-Hopf algebra which is more general than a Hopf algebra. Then we construct the supersymmetry algebra via the adjoint action on this semi-Hopf algebra. As a result we have a supersymmetry theory with quantum gauge group, i.e., quantised enveloping algebra of a simple Lie algebra. For the example, we construct the Lagrangian N=1 and N=2 supersymmetry.