On analogies between algebraic groups and groups of finite Morley rank

TL;DR

This paper explores the structural similarities between algebraic groups and groups of finite Morley rank, establishing new properties of centralizers and applying these to understand minimal simple groups, Borel subgroups, Weyl groups, and automorphisms.

Contribution

It proves that centralizers of decent tori in connected groups of finite Morley rank are connected and applies this to analyze minimal simple groups and their subgroup structures.

Findings

Centralizers of decent tori are connected in finite Morley rank groups.

Provides new insights into the structure of minimal connected simple groups.

Describes properties of Borel subgroups, Weyl groups, and toral automorphisms.

Abstract

We prove that in a connected group of finite Morley rank the centralizers of decent tori are connected. We then apply this result to the analysis of minimal connected simple groups of finite Morley rank. Our applications include general covering properties by Borel subgroups, the description of Weyl groups and the analysis of toral automorphisms.