Centers of Generalized Quantum Groups

TL;DR

This paper studies generalized quantum groups with finite root systems, establishing a Harish-Chandra type theorem that characterizes their centers, advancing understanding of their algebraic structure.

Contribution

It introduces a Harish-Chandra type theorem for the (skew) center of generalized quantum groups with finite root systems.

Findings

Established a Harish-Chandra type theorem for centers of generalized quantum groups.

Characterized the (skew) center structure of these quantum groups.

Extended classical results to a broader class of quantum groups.

Abstract

This paper treats the generalized quantum group $U=U(\chi,\pi)$ with a bi-homomorphism $\chi$ for which the corresponding generalized root system is a finite set. We establish a Harish-Chandra type theorem describing the (skew) center of $U$.