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2011 Matrads, biassociahedra, and A∞-bialgebras
Samson Saneblidze, Ronald Umble
Homology Homotopy Appl. 13(1): 1-57 (2011).

Abstract

We introduce the notion of a matrad $M=\{M_{n,m}\}$ whose submodules $M_{*,1}$ and $M_{1,*}$ are non-$\Sigma$ operads. We define the free matrad $\mathcal{H}_\infty$ generated by a singleton $\theta^n_m$ in each bidegree $(m,n)$ and realize $\mathcal{H}_\infty$ as the cellular chains on a new family of polytopes $\{KK_{n,m}=KK_{m,n}\}$, called biassociahedra, of which $KK_{n,1}$ is the associahedron $K_n$. We construct the universal enveloping functor from matrads to PROPs and define an $A_\infty$-bialgebra as an algebra over $\mathcal{H}_\infty$.

Citation

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Samson Saneblidze. Ronald Umble. "Matrads, biassociahedra, and A∞-bialgebras." Homology Homotopy Appl. 13 (1) 1 - 57, 2011.

Information

Published: 2011
First available in Project Euclid: 29 July 2011

Subjects:
Primary: 55P35, 55P99
Secondary: 52B05

Rights: Copyright © 2011 International Press of Boston

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Vol.13 • No. 1 • 2011
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