Boardman-Vogt tensor products of absolutely free operads

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-02477552
Contributor : Vladimir Dotsenko <>
Submitted on : Thursday, February 13, 2020 - 2:36:21 PM
Last modification on : Friday, February 14, 2020 - 1:36:52 AM

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

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