Structure Of Hyperbolic Unitary Groups - I. Elementary Subgroups

Abstract

. This is the first in the series of papers dedicated to the structure of hyperbolic unitary groups over form rings and their subgroups. In this part we recall foundations of the theory and study elementary subgroup of the hyperbolic unitary group over a ring. In particular, using a variant of Suslin's patching method, we prove standard commutator formulae for relative elementary subgroups. 1991 Mathematics Subject Classification. 20G35, 20H35. Key words and phrases. Unitary group, Unitary transvections, Elementary subgroup. The second-named author gratefully acknowledges the support of the Alexander von Humboldt-Stiftung and the SFB 343 and the hospitality of the Universitat Bielefeld during the preparation of the present article. Typeset by A M S-T E X 2 a.bak, n.a.vavilov Introduction In this series of papers we intend to systematically study subgroups of hyperbolic unitary groups U(2n; R; ) over a form ring (R; ), corresponding to a symmetry (see [B1] -- [B3], [Ba3], [HO'M])...