On the equations defining affine algebraic groups

TL;DR

This paper investigates how to derive canonical generators and relations for the coordinate algebras of connected affine algebraic groups, aiming to better understand their algebraic structure.

Contribution

It introduces a method to find canonical presentations of coordinate algebras based on the group structure, advancing the understanding of algebraic group equations.

Findings

Established a canonical form for coordinate algebra presentations

Provided explicit relations defining affine algebraic groups

Enhanced the algebraic understanding of group structures

Abstract

For the coordinate algebras of connected affine algebraic groups, we explore the problem of finding a presentation by generators and relations canonically determined by the group structure.