Generalized bialgebras and triples of operads Export

@misc{citeulike:968373, abstract = {We introduce the notion of generalized bialgebra, which includes the classical notion of bialgebra (Hopf algebra) and many others. We prove that, under some mild conditions, a connected generalized bialgebra is completely determined by its primitive part. This structure theorem extends the classical Poincar\'e-Birkhoff-Witt theorem and the Cartier-Milnor-Moore theorem, valid for cocommutative bialgebras, to a large class of generalized bialgebras. Technically we work in the theory of operads which permits us to give a conceptual proof of our main theorem. It unifies several results, generalizing PBW and CMM, scattered in the literature. We treat many explicit examples and suggest a few conjectures.}, archivePrefix = {arXiv}, author = {Loday, Jean-Louis}, citeulike-article-id = {968373}, citeulike-linkout-0 = {http://arxiv.org/abs/math/0611885}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/0611885}, day = {28}, eprint = {math/0611885}, keywords = {bialgebras, operads}, month = {Nov}, posted-at = {2006-11-30 08:34:37}, priority = {3}, title = {Generalized bialgebras and triples of operads}, url = {http://arxiv.org/abs/math/0611885}, year = {2006} }

TY - ELEC ID - citeulike:968373 L3 - citeulike-article-id:968373 N2 - We introduce the notion of generalized bialgebra, which includes the classical notion of bialgebra (Hopf algebra) and many others. We prove that, under some mild conditions, a connected generalized bialgebra is completely determined by its primitive part. This structure theorem extends the classical Poincar\'e-Birkhoff-Witt theorem and the Cartier-Milnor-Moore theorem, valid for cocommutative bialgebras, to a large class of generalized bialgebras. Technically we work in the theory of operads which permits us to give a conceptual proof of our main theorem. It unifies several results, generalizing PBW and CMM, scattered in the literature. We treat many explicit examples and suggest a few conjectures. TI - Generalized bialgebras and triples of operads KW - bialgebras KW - operads AU - Loday, Jean-Louis PY - 2006/Nov/28/ UR - http://arxiv.org/abs/math/0611885 ER -