Geodesic
Racks as multiplicative graphs
Homology, homotopy, and applications, Tome 20 (2018) no. 2, pp. 239-257.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2018.v20.n2.a12
Classification : 05C99, 16T05, 20N99
Keywords: rack, multiplicative graph, Loday–Pirashvili category, Leibniz algebra 
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     author = {Jacob Mostovoy},
     title = {Racks as multiplicative graphs},
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     pages = {239--257},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2018.v20.n2.a12/}
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Jacob Mostovoy. Racks as multiplicative graphs. Homology, homotopy, and applications, Tome 20 (2018) no. 2, pp. 239-257. doi : 10.4310/HHA.2018.v20.n2.a12. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2018.v20.n2.a12/

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