Homology, Homotopy and Applications

Volume 17 (2015)

Number 1

Torsors and the Quillen-Barr-Beck cohomology for restricted Lie algebras

Pages: 203 – 234

DOI: http://dx.doi.org/10.4310/HHA.2015.v17.n1.a10

Author

Ioannis Dokas (Department of Mathematics and Statistics, University Of Cyprus, Nicosia, Cyprus)

Abstract

In this paper we study Duskin-Glenn torsor cohomology in the context of restricted Lie algebras. In particular, we give an interpretation of the torsor cohomology groups which appear in Cegarra-Aznar’s eight-term exact sequence. Thus, we prove a classification theorem for the second Quillen-Barr-Beck cohomology in terms of $2$-fold extensions of restricted Lie algebras.

Keywords

restricted Lie algebra, Quillen-Barr-Beck cohomology, torsor, crossed module

2010 Mathematics Subject Classification

17B50, 17B55, 18C15, 18G30

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Published 18 May 2015