Characteristic classes for cohomology of split Hopf algebra extensions

Details Characteristic classes for cohomology of split Hopf algebra extensions Characteristic classes for cohomology of split Hopf algebra extensions

2010-01-31

arxiv.org/abs/1002.0098v2

Journal of Algebra, Volume 332, Issue 1, 15 April 2011, Pages 366-385

Mathematics

Algebraic Topology

22 pages

Scientific paper

We introduce characteristic classes for the spectral sequence associated to a split short exact sequence of Hopf algebras. We show that these characteristic classes can be seen as obstructions for the vanishing of differentials in the spectral sequence and prove a decomposition theorem. We also interpret our results in the settings of group and Lie algebra extensions and prove some interesting corollaries concerning the collapse of the (Lyndon-)Hochschild-Serre spectral sequence and the order of characteristic classes.

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