Homology, Homotopy and Applications

Volume 11 (2009)

Number 1

On $H*(\mathcal{C}; k^×)$ for fusion systems

Pages: 203 – 218

DOI: http://dx.doi.org/10.4310/HHA.2009.v11.n1.a10

Author

Markus Linckelmann (Department of Mathematical Sciences, University of Aberdeen, Scotland, United Kingdom)

Abstract

We give a cohomological criterion for the existence and uniqueness of solutions of the $2$-cocycle gluing problem in block theory. The existence of a solution for the $2$-cocycle gluing problem is further reduced to a property of fusion systems of certain finite groups associated with the fusion system of a block.

Keywords

fusion system; block; 2-cocycle

2010 Mathematics Subject Classification

16E40, 18G40, 20C20

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