Boardman-Vogt tensor products of absolutely free operads

Murray Bremner (1) , Vladimir Dotsenko (2, 3)

1 U of S - University of Saskatchewan [Saskatoon, Canada]
2 Trinity College Dublin
3 CINVESTAV - Centro de Investigacion y de Estudios Avanzados del Instituto Politécnico Nacional

We establish a combinatorial model for the Boardman--Vogt tensor product of several absolutely free operads, that is free symmetric operads that are also free as $\mathbb{S}$-modules. Our results imply that such a tensor product is always a free $\mathbb{S}$-module, in contrast with the results of Kock and Bremner--Madariaga on hidden commutativity for the Boardman--Vogt tensor square of the operad of non-unital associative algebras.

Domaines: Mathématiques [math]; K-théorie et homologie [math.KT]; Catégories et ensembles [math.CT]; Combinatoire [math.CO]; Topologie algébrique [math.AT]

Murray Bremner, Vladimir Dotsenko. Boardman-Vogt tensor products of absolutely free operads. Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, In press, ⟨10.1017/prm.2018.60⟩. ⟨hal-02477552⟩