On the center of two-parameter (v,t)-quantum groups

TL;DR

This paper investigates the structure of the center of two-parameter quantum groups of finite type using an analogue of the Harish-Chandra homomorphism, linking it to the one-parameter case.

Contribution

It provides a description of the center of two-parameter quantum groups by extending the Harish-Chandra homomorphism approach from the one-parameter case.

Findings

Describes the center of two-parameter quantum groups of finite type.

Establishes a connection between one-parameter and two-parameter quantum groups.

Provides a Harish-Chandra homomorphism analogue for the two-parameter case.

Abstract

This paper mainly considers the center of two-parameter quantum group U_{v,t} of finite type via an analogue of the Harish-Chandra homomorphism. Through combining the connection between one-parameter quantum group case and two-parameter quantum group case, we get the description of center in the sense of Harish-Chandra homomorphism.