Modified Steinberg Relations for the Group J4

Gernot Stroth and Richard Weiss
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Gernot Stroth: Freien Universität Berlin, II. Mathematisches Institut der
Richard Weiss: Tufts University, Department of Mathematics

A chapter in Geometries and Groups, 1988, pp 513-525 from Springer

Abstract: Abstract Let Φ be a root system of type D 5 and let Δ ⊆ Φ be a fundamental system of roots, which we label with the integers 1,2,…, 5. For each i ∈ Δ there is a unique involution αi in the corresponding root group of the Chevalley group D 5(2). The opposite root corresponds to an involution we will call α–i . We let w i = α i α–i for each i ∈ Δ and assume that the labels are chosen so that (w 1 w 2)3 = (w 2 w 3)3 = (w 3 w 4)3 = (w 3 w 5)3 = 1. We will denote commutators of the elements α1,…, α5 with multiple subscripts, i.e. α12 = [α1, α2], α123 = [α12, α3] etc. The elements α1,…, α5, w 5,…,w 5 generate D 5(2) and satisfy the Steinberg relations [3, p. 190], which may be used to define D 5(2) abstractly.

Date: 1988
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DOI: 10.1007/978-94-009-4017-8_19

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