Quantum Group Gauge Theories and Covariant Quantum Algebras

TL;DR

This paper develops an algebraic framework for quantum group gauge theories using the $R$-matrix approach, constructing quantum deformations of various gauge models and Einstein gravity with covariant quantum algebras.

Contribution

It introduces a novel algebraic formulation of quantum group gauge models, including quantum deformations of topological and gravitational theories.

Findings

Constructed quantum deformations of Chern-Simons models

Developed noncommutative gauge theories with quantum group symmetry

Generated covariant quantum algebras from noncommutative fields

Abstract

The algebraic formulation of the quantum group gauge models in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider gauge groups taking values in the quantum groups and noncommutative gauge fields transformed as comodules under the coaction of the gauge quantum group $ G_{q}$. Using this approach we construct the quantum deformations of the topological Chern-Simons models, non-abelian gauge theories and the Einstein gravity. The noncommutative fields in these models generate $ G_{q}$-covariant quantum algebras.