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Coassociative magmatic bialgebras and the Fine numbers |
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| Authors: | Ralf Holtkamp Jean-Louis Loday María Ronco |
| Institution: | 1. Fakult?t für Mathematik, Ruhr-Universit?t, 44780, Bochum, Germany 2. Institut de Recherche Mathématique Avancée, CNRS et Université Louis Pasteur, 7 rue R. Descartes, 67084, Strasbourg Cedex, France 3. Departamento de Matematicas, Facultad de Ciencias, Universidad de Valparaiso, Avda. Gran Bretana, 1091, Valparaiso, Chile |
| Abstract: | We prove a structure theorem for the connected coassociative magmatic bialgebras. The space of primitive elements is an algebra over an operad called the primitive operad. We prove that the primitive operad is magmatic generated by n−2 operations of arity n. The dimension of the space of all the n-ary operations of this primitive operad turns out to be the Fine number F n−1. In short, the triple of operads (As, Mag, MagFine) is good. The third author work is partially supported by FONDECYT Project 1060224 |
| Keywords: | Bialgebra Generalized bialgebra Hopf algebra Cartier– Milnor– Moore Poincaré– Birkhoff– Witt Magmatic Operad Fine number Pre-Lie algebra |
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