Scheme theory for groups and Lie algebras

TL;DR

This paper introduces a scheme-theoretic approach to algebraic geometry for groups and Lie algebras, providing a geometric framework to analyze algebraic sets defined by equations on these structures.

Contribution

It develops a free coordinates approach linking scheme theory to the study of algebraic sets in groups and Lie algebras, extending classical algebraic geometry methods.

Findings

Establishes a scheme-theoretic framework for groups and Lie algebras.

Provides a geometric perspective on algebraic equations in these structures.

Lays groundwork for further geometric analysis of finite groups.

Abstract

Algebraic geometry for groups and Lie algebraic has been recently defined and studied by many authors on the purpose to study set defined by algebraic equations on abstract groups and Lie algebras. The purpose of this paper is to present a free coordinates approach of this problem. This must be related to the theory of schemes in classical algebraic geometry, and provide a geomotric framework to study finite groups