Structure of Chevalley groups over rings via universal localization

By Alexei Stepanov. 2013

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Abstract In the current article we study the structure of a Chevalley group G ( R ) over a commutative ring R. We generalize and improve the following results on: • the standard, relative, and multi-relative commutator formulas; • the nilpotent structure of [relative] K 1 ; • the bounded word length of commutators. To this end we enlarge the elementary group, construct a generic element for the extended elementary group, and use localization in the universal ring. The key step is a construction of a generic element for the principal congruence subgroup, corresponding to a principal ideal.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/eac0052a7c109613c9f2da2e86bf0f97c7c370c1