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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
On a Hopf operad containing the Poisson operad

Frédéric Chapoton

Algebraic & Geometric Topology 3 (2003) 1257–1273

arXiv: math.QA/0212021

Abstract

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
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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