Algebraic structure of multi-parameter quantum groups

TL;DR

This paper explores the algebraic structure of multi-parameter quantum groups, extending known results for standard quantum groups and analyzing their primitive spectra and Poisson structures.

Contribution

It generalizes the classification of primitive spectra to multi-parameter quantum groups and compares it with Poisson geometric structures.

Findings

Primitive spectrum of C_p[G] is explicitly calculated.

Comparison made between algebraic spectra and Poisson geometric leaves.

Extends Joseph's classification to multi-parameter quantum groups.

Abstract

Multi-parameter versions U_p(g) and C_p[G] of the standard quantum groups U_q(g) and C_q[G] are considered where G is a semi-simple connected complex algebraic group and g is the Lie algebra of G. The primitive spectrum of C_p[G] is calculated, generalizing a result of Joseph for the standard quantum groups. This classification is compared with the classification of symplectic leaves for the associated Poisson structure on G.