English

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 LM\mathcal{LM}. Finally, we discuss the integration of Lie algebras in LM\mathcal{LM} in the context of multiplicative graphs and augmented racks.

Keywords

Cite

@article{arxiv.1707.01787,
  title  = {Racks as multiplicative graphs},
  author = {Jacob Mostovoy},
  journal= {arXiv preprint arXiv:1707.01787},
  year   = {2017}
}
R2 v1 2026-06-22T20:39:40.229Z