Rack homology and conjectural Leibniz homology
K-Theory and Homology
2014-02-10 v1
Abstract
This article presents results being consistent with conjectures of J.-L. Loday about the existence and properties of a Leibniz homology for groups. Introducing L-sets we prove that (pointed) rack homology has properties this conjectural Leibniz homology should satisfy, namely the existence of a coZinbiel coalgebra structure on rack homology and the existence of a non trivial natural cocommutative coalgebra morphism from the rack homology of a group to its Eilenberg-MacLane homology. The end of the paper treats the particular cases of the linear group and of abelian groups. We prove the existence of a connected coZinbiel-associative bialgebra structure on their rack homology.
Keywords
Cite
@article{arxiv.1402.1625,
title = {Rack homology and conjectural Leibniz homology},
author = {Simon Covez},
journal= {arXiv preprint arXiv:1402.1625},
year = {2014}
}