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Boardman–Vogt tensor products of absolutely free operads

Published online by Cambridge University Press:  26 January 2019

Murray Bremner
Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Canada (bremner@math.usask.ca)
Vladimir Dotsenko
Affiliation:
School of Mathematics, Trinity College Dublin, Ireland and Departamento de Matemáticas, CINVESTAV-IPN, Col. San Pedro Zacatenco, México, D.F., CP 07360, Mexico (vdots@maths.tcd.ie)
Corresponding

Abstract

To the memory of Trevor Evans (1925–1991),

the pioneer of interchange laws in universal algebra

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 𝕊-modules. Our results imply that such a tensor product is always a free 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.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2019

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