Galois theory and commutators

Details Galois theory and commutators Galois theory and commutators

2011-04-04

arxiv.org/abs/1104.0518v1

Algebra Universalis 65 (2011), no. 2, 161-177

Mathematics

Rings and Algebras

14 pages

Scientific paper

10.1007/s00012-011-0121-8

We prove that the relative commutator with respect to a subvariety of a variety of Omega-groups introduced by the first author can be described in terms of categorical Galois theory. This extends the known correspondence between the Froehlich-Lue and the Janelidze-Kelly notions of central extension. As an example outside the context of Omega-groups we study the reflection of the category of loops to the category of groups where we obtain an interpretation of the associator as a relative commutator.

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