Associahedra, cellular $W$-construction and products of $A_\infty$-algebras
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- by Martin Markl and Steve Shnider PDF
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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.References
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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
- 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 - © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 2353-2372
- MSC (2000): Primary 18D50, 55U99
- DOI: https://doi.org/10.1090/S0002-9947-05-04006-7
- MathSciNet review: 2204035