Algebraic Structures Related to Reflection Equations

TL;DR

This paper introduces quadratic algebras associated with reflection equations, exploring their properties and generalizations within the framework of quantum group comodule algebras, exemplified by $F_q(GL(2))$.

Contribution

It develops a detailed study of quadratic algebras related to reflection equations, including their structure, representations, and potential generalizations, within quantum group theory.

Findings

Identified properties of the algebras such as center and realizations

Analyzed representations and real forms of the algebras

Discussed fusion procedures and algebra generalizations

Abstract

Quadratic algebras related to the reflection equations are introduced. They are quantum group comodule algebras. The quantum group $F_q(GL(2))$ is taken as the example. The properties of the algebras (center, representations, realizations, real forms, fusion procedure etc) as well as the generalizations are discussed.