The yoga of commutators

Abstract

In the present paper we discuss some recent versions of localisation methods for calculations in the groups of points of algebraic-like and classical-like groups. Namely, we describe relative localisation, universal localisation, and enhanced versions of localisation-completion. Apart from the general strategic description of these methods, we state some typical technical results of the conjugation calculus and the commutator calculus. Also, we state several recent results obtained therewith, such as relative standard commutator formulae, bounded width of commutators, with respect to the elementary generators, and nilpotent filtrations of congruence subgroups. Overall, this shows that localisation methods can be much more efficient, than expected.

References in corpus (2)

• A user's guide to basic knot and link theory
• Relative commutator calculus in Chevalley groups

Cited by in corpus (10)

• Structure of Chevalley groups over rings via universal localization
• Word equations in simple groups and polynomial equations in simple algebras
• Commutator width in Chevalley groups
• Generation of relative commutator subgroups in Chevalley groups. II
• Commutators of relative and unrelative elementary subgroups in Chevalley groups
• Commutators of relative and unrelative elementary unitary groups
• Yoga of Commutators in Roy's Elementary Orthogonal Group
• Multiple Commutator Formulas for Unitary Groups
• Local-global principle for congruence subgroups of Chevalley groups
• Locally isotropic elementary groups