Root graded groups of type H₃ and H₄

2024/08/13 by Berg, Lennart, Wiedemann, Torben · 1 citation
#20E42 (Primary) 17C05 #20F40 #51C05 (Secondary) #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2408.06745

Abstract

Using the well-known realisation of the root system H₄ as a folding of E₈ , one can construct examples of H₄ -graded groups from Chevalley groups of type E₈ . Such Chevalley groups are defined over a commutative ring R , and the root groups of the resulting H₄ -grading are coordinatised by R × R . We show that every H₄ -graded group arises as the folding of an E₈ -graded group, or in other words, that it is coordinatised by R × R for some commutative ring R . We also prove similar assertions for (D₆, H₃) in place of (E₈, H₄) .

Cited by

• Locally isotropic Steinberg groups II. Schur multipliers

Related

• Root Graded Groups
• Root graded groups revisited
• Property (T) for groups graded by root systems
• Normalizer of the Chevalley group of type E₇
• Automorphisms of Chevalley groups over commutative rings