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arXiv · 1912.06563

Operads on graphs: extending the pre-Lie operad and general construction

Jean-Christophe Aval·Samuele Giraudo·Théo Karaboghossian·Adrian Tanasa
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Abstract

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.

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Jean-Christophe Aval, Samuele Giraudo, Théo Karaboghossian, Adrian Tanasa. 2019-12-13. Operads on graphs: extending the pre-Lie operad and general construction. https://arxiv.org/abs/1912.06563

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