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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Associahedra, cellular $ W$-construction and products of $ A_\infty$-algebras


Authors: Martin Markl and Steve Shnider
Journal: Trans. Amer. Math. Soc. 358 (2006), 2353-2372
MSC (2000): Primary 18D50, 55U99
Published electronically: December 20, 2005
MathSciNet review: 2204035
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Abstract: The aim of this paper is to construct a functorial tensor product of $ A_\infty$-algebras or, equivalently, an explicit diagonal for the operad of cellular chains, over the integers, of the Stasheff associahedron. These constructions in fact already appeared (Saneblidze and Umble, 2000 and 2002); we will try to give a more conceptual presentation. We also prove that there does not exist a coassociative diagonal.


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Additional Information

Martin Markl
Affiliation: Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Prague 1, The Czech Republic
Email: markl@math.cas.cz

Steve Shnider
Affiliation: Department of Mathematics, Bar Ilan University, Ramat Gan, Israel
Email: shnider@macs.biu.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9947-05-04006-7
PII: S 0002-9947(05)04006-7
Received by editor(s): January 5, 2004
Published electronically: December 20, 2005
Additional Notes: The first author was supported by the grant GA ČR 201/02/1390
The second author was supported by the Israel Academy of Sciences
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.