Operads on graphs: extending the pre-Lie operad and general construction
| Autor: | Aval, Jean-Christophe, Giraudo, Samuele, Karaboghossian, Théo, Tanasa, Adrian |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The overall aim of this paper is to define a structure of graph operads, thus generalizing the celebrated pre-Lie operad on rooted trees. More precisely, we define two operads on multigraphs, and exhibit a non trivial link between them and the pre-Lie and Kontsevich- Willwacher operads. We study one of these operads in more detail. While its structure is too involved to exhibit a description by generators and relations, we show that it has interesting finitely generated sub-operads, with links with the commutative and the magmatic commutative operads. In particular, one of them is Koszul and this allows us to compute its Koszul dual. Finally, we introduce a new framework on species and operads and a general way to define operads on multigraphs. Comment: 28 pages, 12 figures. 3rd version, major changes |
| Databáze: | arXiv |
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