Formulas for the Connes-Moscovici Hopf algebra

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dc.creatorMenous, Frederic
dc.date2008-12-15
dc.date.accessioned2026-07-07T12:12:56Z
dc.date.available2026-07-07T12:12:56Z
dc.descriptionWe give explicit formulas for the coproduct and the antipode in the Connes-Moscovici Hopf algebra $\mathcal{H}_{\tmop{CM}}$. To do so, we first restrict ourselves to a sub-Hopf algebra $\mathcal{H}^1_{\tmop{CM}}$ containing the nontrivial elements, namely those for which the coproduct and the antipode are nontrivial. There are two ways to obtain explicit formulas. On one hand, the algebra $\mathcal{H}^1_{\tmop{CM}}$ is isomorphic to the Faà di Bruno Hopf algebra of coordinates on the group of identity-tangent diffeomorphism and computations become easy using substitution automorphisms rather than diffeomorphisms. On the other hand, the algebra $\mathcal{H}^1_{\tmop{CM}}$ is isomorphic to a sub-Hopf algebra of the classical shuffle Hopf algebra which appears naturally in resummation theory, in the framework of formal and analytic conjugacy of vector fields. Using the very simple structure of the shuffle Hopf algebra, we derive once again explicit formulas for the coproduct and the antipode in $\mathcal{H}^1_{\tmop{CM}}$.
dc.identifierhttps://arxiv.org/abs/0812.2845
dc.identifierhttp://arxiv.org/abs/0812.2845
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210706
dc.subjectDynamical Systems
dc.subjectCombinatorics
dc.titleFormulas for the Connes-Moscovici Hopf algebra
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