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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fine structures inside the PreLie operad


Author: Frédéric Chapoton
Journal: Proc. Amer. Math. Soc. 141 (2013), 3723-3737
MSC (2010): Primary 05C05, 18D50; Secondary 17A30
Published electronically: July 16, 2013
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Abstract: This article aims at a detailed analysis of the $ \operatorname {PreLie}$ operad. We obtain a concrete description (as a morphism) of the relationship between the anticyclic structure of $ \operatorname {PreLie}$ and the generators of $ \operatorname {PreLie}$ as a $ \operatorname {Lie}$-module, which was previously known only at the level of characters. Building on this, we obtain a surprising inclusion of the cyclic Lie module in the $ \operatorname {PreLie}$ operad. We conjecture that the image of this inclusion generates an interesting free sub-operad.


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Additional Information

Frédéric Chapoton
Affiliation: Institut Camille Jordan, Université Claude Bernard Lyon 1, 21 Avenue Claude Bernard, 69622 Villeurbanne Cedex, France

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11655-2
PII: S 0002-9939(2013)11655-2
Received by editor(s): December 12, 2011
Received by editor(s) in revised form: January 17, 2012
Published electronically: July 16, 2013
Communicated by: Jim Haglund
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.