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L'algebre de Hopf bitensorielle

Dominique Manchon
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Abstract

Nous construisons pour tout corps k de caracteristique zero un foncteur de la categorie des k-espaces vectoriels dans la categorie des k-algebres de Hopf pointees, qui a tout espace vectoriel V associe son algebre de Hopf bitensorielle pointee A(V). Cette algebre de Hopf est graduee, verifie une propriete universelle, et contient une famille remarquable d'elements primitifs P. Nous conjecturons que P engendre l'algebre de Lie des elements primitifs de A(V). Enfin lorsque V est de dimension finie nous mettons en evidence un couplage de Hopf entre A(V) et A(V*) dont le noyau contient l'ideal (de Hopf) engendre par les elements de P de degre au moins egal a 2.

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Dominique Manchon. 1996-06-24. L'algebre de Hopf bitensorielle. https://arxiv.org/abs/q-alg/9606017

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