On a Hopf operad containing the Poisson operad

A new Hopf operad $Ram$ is introduced, which contains both the well-known Poisson operad and the Bessel operad introduced previously by the author. Besides, a structure of cooperad $R$ is introduced on a collection of algebras given by generators and relations which have some similarity with the Arnold relations for the cohomology of the type $A$ hyperplane arrangement. A map from the operad $Ram$ to the dual operad of $R$ is defined which we conjecture to be a isomorphism.

Keywords

Hopf operad, coalgebra, chain complex

Mathematical Subject Classification 2000

Primary: 18D50

Secondary: 16W30

References

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Publication

Received: 20 January 2003

Revised: 12 December 2003

Accepted: 18 December 2003

Published: 20 December 2003

Authors

Frédéric Chapoton
LACIM Université du Québec à Montréal CP 8888 Succursale centre ville Montréal Québec H3C 3P8 Canada

Volume 3, issue 2 (2003)

Frédéric Chapoton