Another presentation for symplectic Steinberg groups

作者：Lavrenov Andrei^*

来源：Journal of Pure and Applied Algebra, 2015, 219(9): 3755-3780.

DOI：10.1016/j.jpaa.2014.12.021

We solve a classical problem of centrality of symplectic K-2, namely we show that for an arbitrary commutative ring R, l >= 3, the symplectic Steinberg group StSp(2l, 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 K(2)Sp(2l, R) as a kernel of the above 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.

• 出版日期2015-9