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Associahedra, cellular  -construction and products of  -algebras
Author(s):
Martin
Markl;
Steve
Shnider
Journal:
Trans. Amer. Math. Soc.
358
(2006),
2353-2372.
MSC (2000):
Primary 18D50, 55U99
Posted:
December 20, 2005
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Abstract:
The aim of this paper is to construct a functorial tensor product of  -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, Zitná 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:
10.1090/S0002-9947-05-04006-7
PII:
S 0002-9947(05)04006-7
Received by editor(s):
January 5, 2004
Posted:
December 20, 2005
Additional Notes:
The first author was supported by the grant GA CR 201/02/1390
The second author was supported by the Israel Academy of Sciences
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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