On démontre un théorème de structure pour les algèbres de Hopf colibres : une telle algèbre de Hopf est isomorphe à l'algèbre diptère enveloppante de sa partie primitive. Une algèbre diptère est une algèbre associative munie d'une structure de module à gauche sur elle-même. Ce résultat est une conséquence d'un analogue, dans le contexte non-cocommutatif, du théorème de Poincaré–Birkhoff–Witt et du théorème de Milnor–Moore.
We prove a structure theorem for the cofree Hopf algebras: such a Hopf algebra is the universal enveloping dipterous algebra of its primitive part. A dipterous algebra is an associative algebra equipped with a structure of left module over itself. This theorem is a consequence of an analogue, in the non-cocommutative framework, of the Poincaré–Birkhoff–Witt theorem and of the Milnor–Moore theorem.
Publié le :
Jean-Louis Loday 1 ; Marı́a Ronco 2
@article{CRMATH_2003__337_3_153_0,
author = {Jean-Louis Loday and Mar{\i}́a Ronco},
title = {Alg\`ebres de {Hopf} colibres},
journal = {Comptes Rendus. Math\'ematique},
pages = {153--158},
publisher = {Elsevier},
volume = {337},
number = {3},
year = {2003},
doi = {10.1016/S1631-073X(03)00288-7},
language = {fr},
}
Jean-Louis Loday; Marı́a Ronco. Algèbres de Hopf colibres. Comptes Rendus. Mathématique, Volume 337 (2003) no. 3, pp. 153-158. doi : 10.1016/S1631-073X(03)00288-7. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00288-7/
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