Differential calculus and gauge transformations on a deformed space

TL;DR

This paper explores how gauge transformations and Lie algebra representations can be extended to deformed coordinate spaces using twisted Hopf algebras, enabling the construction of invariant Lagrangians.

Contribution

It introduces a framework for gauge theories on deformed spaces using twisted Hopf algebras, extending classical Lie algebra representations.

Findings

Deformed gauge transformations are compatible with twisted Hopf algebra structures.

Representation theory necessitates working within a deformed Lie algebra.

Invariant Lagrangians can be constructed on deformed spaces using this approach.

Abstract

Deformed gauge transformations on deformed coordinate spaces are considered for any Lie algebra. The representation theory of this gauge group forces us to work in a deformed Lie algebra as well. This deformation rests on a twisted Hopf algebra, thus we can represent a twisted Hopf algebra on deformed spaces. That leads to the construction of Lagrangian invariant under a twisted Lie algebra.