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Non-Abelian K-Theory for Chevalley Groups over Rings

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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 K1; (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.

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Authors and Affiliations

  1. St.Petersburg State University, St.Petersburg State Electrotechnical University, St.Petersburg, Russia

    A. V. Stepanov

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  1. A. V. Stepanov
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Correspondence to A. V. Stepanov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 423, 2014, pp. 244–263.

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Stepanov, A.V. Non-Abelian K-Theory for Chevalley Groups over Rings. J Math Sci 209, 645–656 (2015). https://doi.org/10.1007/s10958-015-2518-y

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