NON-ABELIAN K-THEORY FOR CHEVALLEY GROUPS OVER RINGS

摘要

The article contains a survey of the recent author's results on the structure of a Chevalley group G{R) over a ring R. They generalize and improve previously known results on: (1) the relative local-global principle; (2) generators of a relative elementary group; (3) relative multicommutator formulas; (4) the nilpotent structure of a relative K_1; (5) the bounded length of commutators. The proof of the first two items is based on computations with generators of the elementary group translated into the language of parabolic subgroups. The other results are proved by means of enlarging a relative elementary group, constructing a generic element, and using the localization procedure in the universal ring. Bibliography: 40 titles.