Racks as multiplicative graphs
| Autor: | Jacob Mostovoy |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Leibniz algebra
Pure mathematics 010102 general mathematics Multiplicative function Context (language use) Group Theory (math.GR) Group algebra Homology (mathematics) Hopf algebra 01 natural sciences Mathematics::Geometric Topology Computer Science::Robotics Mathematics (miscellaneous) Mathematics::Category Theory Mathematics::Quantum Algebra Lie algebra FOS: Mathematics Point (geometry) 0101 mathematics Mathematics - Group Theory Mathematics |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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