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Root Graded Groups

Paper Title:

Root Graded Groups

Published on:

2 April 2024

Primary Category:

Group Theory

Paper Authors:

Torben Wiedemann


Key Details

Root graded groups are graded by finite root systems

Prominent examples are Chevalley groups over commutative associative rings

We show root graded groups of rank ≥3 can be coordinatized by algebraic structures satisfying the Chevalley commutator formula

This generalizes Tits' classification of spherical buildings to non-division structures

We use a new computational blueprint technique to prove this in a characteristic-free way

AI generated summary

Root Graded Groups

We define root graded groups, graded by finite root systems, which generalize concepts like Jacques Tits' RGD-systems. The most prominent examples are Chevalley groups over commutative associative rings. Our main result is that every root graded group of rank at least 3 can be coordinatized by some algebraic structure satisfying a variation of the Chevalley commutator formula, generalizing Tits' classification of thick irreducible spherical buildings.

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