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.
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@article{CRMATH_2003__337_3_153_0,
author = {Loday, Jean-Louis and Ronco, Mar{\i}́a},
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},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(03)00288-7/}
}
TY - JOUR AU - Loday, Jean-Louis AU - Ronco, Marı́a TI - Algèbres de Hopf colibres JO - Comptes Rendus. Mathématique PY - 2003 SP - 153 EP - 158 VL - 337 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(03)00288-7/ DO - 10.1016/S1631-073X(03)00288-7 LA - fr ID - CRMATH_2003__337_3_153_0 ER -
Loday, Jean-Louis; Ronco, Marı́a. Algèbres de Hopf colibres. Comptes Rendus. Mathématique, Tome 337 (2003) no. 3, pp. 153-158. doi : 10.1016/S1631-073X(03)00288-7. http://archive.numdam.org/articles/10.1016/S1631-073X(03)00288-7/
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