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arXiv · 0710.0572

The diagonal of the Stasheff polytope

Jean-Louis Loday
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Abstract

We construct an A-infinity structure on the tensor product of two A-infinity algebras by using the simplicial decomposition of the Stasheff polytope. The key point is the construction of an operad AA-infinity based on the simplicial Stasheff polytope. The operad AA-infinity admits a coassociative diagonal and the operad A-infinity is a retract by deformation of it. We compare these constructions with analogous constructions due to Saneblidze-Umble and Markl-Shnider based on the Boardman-Vogt cubical decomposition of the Stasheff polytope.

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Jean-Louis Loday. 2007-10-23. The diagonal of the Stasheff polytope. https://arxiv.org/abs/0710.0572

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