On a Hopf operad containing the Poisson operad

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.