L'algebre de hopf bitensorielle |
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Authors: | Dominique Manchon |
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Affiliation: | CNRS , Institut Elie Cartan , BP 239, Vandoeuvre les Nancy Cedex, France, 54506 E-mail: manchon@iecn.u-nancy.fr |
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Abstract: | For any field k of zero characteristic we give a functor from the category of k-vector spaces into the category of k-Hopf algebras, attaching to any vector space V its bitensorial pointed Hopf algebra Av. This Hopf algebra is graded, fulfills a universal property, and contains a remarkable subspace P of primitive elements, which as a conjecture may generate the Lie algebra Prim Av. In case V is finite-dimensional we exhibit a Hopf pairing between Avand Av-whose kernel contains the (Hopf) ideal generated by the elements of P of degree ? 2. |
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