Relations in quantized function algebras

TL;DR

This paper introduces a method to present quantized function algebras of complex reductive groups, including automorphism groups of simple Lie algebras, advancing the understanding of their algebraic structures.

Contribution

It provides new presentations for quantized function algebras of complex reductive groups and their automorphism groups of simple Lie algebras.

Findings

Developed a systematic method for presentations

Applied method to automorphism groups of simple Lie algebras

Enhanced understanding of algebraic structures in quantum groups

Abstract

We develop a method to give presentations of quantized function algebras of complex reductive groups. In particular, we give presentations of quantized function algebras of automorphism groups of finite dimensional simple complex Lie algebras.