Paper Authors:

Torben Wiedemann

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Root graded groups are graded by finite root systems

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Prominent examples are Chevalley groups over commutative associative rings

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

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

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

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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