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Galois theory and commutators

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Everaert, Tomas Van der Linden, Tim [UCL]

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 Frohlich-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.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2011
Language Anglais
Journal information "Algebra universalis" - Vol. 65, no. 2, p. 161-177 (2011)
Peer reviewed yes
Publisher BIRKHAUSER VERLAG AG
issn 0002-5240
Publication status Publié
Affiliation UCL - SST/IRMP - Institut de recherche en mathématique et physique
Keywords Categorical Galois theory ; Semi-abelian category ; Commutator;associator ; Higher central extension
Links
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Bibliographic reference Everaert, Tomas ; Van der Linden, Tim. Galois theory and commutators. In: Algebra universalis, Vol. 65, no. 2, p. 161-177 (2011)
Permanent URL http://hdl.handle.net/2078.1/83373