Higher central extensions and cohomology

Rodelo, Diana; Van der Linden, Tim

http://hdl.handle.net/10400.1/9663

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Authors

Rodelo, Diana

Van der Linden, Tim

Abstract(s)

We establish a Galois-theoretic interpretation of cohomology in semi-abelian categories: cohomology with trivial coefficients classifies central extensions, also in arbitrarily high degrees. This allows us to obtain a duality, in a certain sense, between "internal" homology and "external" cohomology in semiabelian categories. These results depend on a geometric viewpoint of the concept of a higher central extension, as well as the algebraic one in terms of commutators. (C) 2015 Elsevier Inc. All rights reserved.