On a Small Version of the Reflection Equation Algebra

Abstract

We give an alternative presentation of the small version of the reflection equation algebra associated to $G{L}_N$ at both odd and even roots of unity, and use our presentation to classify its irreducible representations. We then describe a family of algebras generalizing the small reflection equation algebra, and consider their application to the study of module categories over $U_q(s{l}_N)$ fusion categories.