Racks as multiplicative graphs
Group Theory
2017-08-03 v2
Abstract
We interpret augmented racks as a certain kind of multiplicative graphs and show that this point of view is natural for defining rack homology. We also define the analogue of the group algebra for these objects; in particular, we see how discrete racks give rise to Hopf algebras and Lie algebras in the Loday-Pirashvili category . Finally, we discuss the integration of Lie algebras in in the context of multiplicative graphs and augmented racks.
Cite
@article{arxiv.1707.01787,
title = {Racks as multiplicative graphs},
author = {Jacob Mostovoy},
journal= {arXiv preprint arXiv:1707.01787},
year = {2017}
}