Artículo
Loday, J.-L.; Ronco, M.O. "A duality between standard simplices and Stasheff polytopes " (2001) Comptes Rendus de l'Academie des Sciences - Series I: Mathematics. 333(2):81-86
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Abstract:
We show that the family of chain modules over the standard simplices can be equipped with an operad structure. Similarly, the family of cochain modules of the Stasheff polytopes can be equipped with an operad structure. We first show that these operads are Koszul dual to each other, and second that they are both Koszul operads. The algebras over the standard simplices operad, called associative trialgebras, are defined by 3 operations and 11 relations. The algebras over the Stasheff polytopes operad, called dendriform trialgebras, are defined by 3 operations and 7 relations. © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.
Registro:
| Documento: | Artículo |
| Título: | A duality between standard simplices and Stasheff polytopes |
| Autor: | Loday, J.-L.; Ronco, M.O. |
| Filiación: | Inst. de Rech. Math. Avancée, CNRS et Univ. Louis Pasteur, 7, rue R. Descartes, 67084 Strasbourg cedex, France Depto. de Matematica Ciclo Basico C., Universidad de Buenos Aires, Pab. 3 Cd. Universitaria Nuñez, 1428 Buenos-Aires, Argentina |
| Año: | 2001 |
| Volumen: | 333 |
| Número: | 2 |
| Página de inicio: | 81 |
| Página de fin: | 86 |
| DOI: | http://dx.doi.org/10.1016/S0764-4442(01)02014-6 |
| Título revista: | Comptes Rendus de l'Academie des Sciences - Series I: Mathematics |
| Título revista abreviado: | C. R. Acad. Sci. Ser. I Math. |
| ISSN: | 07644442 |
| CODEN: | CASME |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07644442_v333_n2_p81_Loday |
Referencias:
- Chapoton, F., (2000) Opérades, polytopes et bigèbres, Thèse, , Université Paris VI
- Ginzburg, V., Kapranov, M., Koszul duality for operads (1994) Duke Math. J., 76 (1), pp. 203-272
- Loday, J.-L., Algèbres ayant deux opérations associatives (digèbres) (1995) C. R. Acad. Sci. Paris, Série I, 321 (2), pp. 141-146
- Loday, J.-L., Dialgebras (2001) Dialgebras and Related Operads Lecture Notes in Math., 1763, pp. 7-66. , Springer-Verlag
- Loday, J.-L., Ronco, M.O., Hopf algebra of the planar binary trees (1998) Adv. Math., 139 (2), pp. 293-309
- Loday, J.-L., Ronco, M.O., Trialgebras, , en préparation
- Proceedings of Renaissance Conferences, Hartford, CT/Luminy, 1995 (1997) Contemp. Math., 202, pp. 37-52. , Providence, RI: Amer. Math. Soc
- Ronco, M.O., A Milnor-Moore theorem for dendriform Hopf algebras (2000) C. R. Acad. Sci. Paris, Série I, 332, pp. 109-114
- Stasheff, J.D., Homotopy associativity of H -spaces. I, II (1963) Trans. Amer. Math. Soc., 108, pp. 275-292
- (1963) Trans. Amer. Math. Soc., 108, pp. 293-312
Citas:
---------- APA ----------
Loday, J.-L. & Ronco, M.O. (2001) . A duality between standard simplices and Stasheff polytopes . Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, 333(2), 81-86.http://dx.doi.org/10.1016/S0764-4442(01)02014-6
---------- CHICAGO ----------
Loday, J.-L., Ronco, M.O. "A duality between standard simplices and Stasheff polytopes " . Comptes Rendus de l'Academie des Sciences - Series I: Mathematics 333, no. 2 (2001) : 81-86.http://dx.doi.org/10.1016/S0764-4442(01)02014-6
---------- MLA ----------
Loday, J.-L., Ronco, M.O. "A duality between standard simplices and Stasheff polytopes " . Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, vol. 333, no. 2, 2001, pp. 81-86.http://dx.doi.org/10.1016/S0764-4442(01)02014-6
---------- VANCOUVER ----------
Loday, J.-L., Ronco, M.O. A duality between standard simplices and Stasheff polytopes . C. R. Acad. Sci. Ser. I Math. 2001;333(2):81-86.http://dx.doi.org/10.1016/S0764-4442(01)02014-6
