2014/05/16 by Andrei Lavrenov, Lavrenov, Andrei · 1 citation
Mathematics · #19C09 #FOS: Mathematics #K-Theory and Homology (math.KT) #math.KT #msc:19C09
paper · pdf · doi:10.48550/arxiv.1405.4296
arxiv created 2014/12/11 · arxiv updated 2014/12/12
We solve a classical problem of centrality of symplectic \mathrm K2, namely we show that for an arbitrary commutative ring R, l≥3 the symplectic Steinberg group StSp(2l, R) as an extension of the elementary symplectic group Ep(2l, R) is a central extension. This allows to conclude that the explicit definition of symplectic K2Sp(2l, R) as a kernel of this extension, i.e. as a group of non-elementary relations among symplectic transvections, coincides with the usual implicit definition via plus-construction. We proceed from van der Kallen's classical paper, where he shows an analogous result for linear K-theory. We find a new set of generators for the symplectic Steinberg group and a defining system of relations among them. In this new presentation it is obvious that the symplectic Steinberg group is a central extension.