Another presentation of orthogonal Steinberg groups

2020/12/22 by Voronetsky, Egor
#19C09 #20G35 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2012.12147

Abstract

We use the pro-group approach to show that StO(M, q) admits van der Kallen's "another presentation", where M is a module over a commutative ring with sufficiently isotropic quadratic form q. Moreover, we construct an analog of ESD-transvections in orthogonal Steinberg pro-groups under some assumptions on their parameters.

Related

• Cosheaves of Steinberg pro-groups
• A presentation of relative unitary Steinberg groups
• Centrality of odd unitary K₂-functor
• Locally isotropic Steinberg groups I. Centrality of the \mathrm K₂-functor
• Distinction of the Steinberg representation