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arXiv · 1707.01787

Racks as multiplicative graphs

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

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Jacob Mostovoy. 2017-07-06. Racks as multiplicative graphs. https://arxiv.org/abs/1707.01787

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