Root graded groups revisited

2024/06/05 by Voronetsky, Egor · 2 citations
#20E42 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2406.03558

Abstract

A group G is called root graded if it has a family of subgroups G_α indexed by roots from a root system Φ satisfying natural conditions similar to Chevalley groups over commutative unital rings. For any such group there is a corresponding algebraic structure (commutative unital ring, associative unital ring, etc.) encoding the commutator relations between G_α. We give a complete description of varieties of such structures for irreducible root systems of rank ≥ 3 excluding \mathsf H₃ and \mathsf H₄. Moreover, we provide a construction of root graded groups for all algebraic structures from these varieties.

Cited by

• Locally isotropic Steinberg groups II. Schur multipliers
• Abstract isomorphisms of isotropic root graded groups over rings

Related

• Root Graded Groups
• Property (T) for groups graded by root systems
• Root graded groups of type H₃ and H₄
• Root systems in number fields
• Central extension of graded Lie algebras