A duality between standard simplices and Stasheff polytopes
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...
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todo:paper_07644442_v333_n2_p81_Loday2023-10-03T15:39:39Z A duality between standard simplices and Stasheff polytopes Loday, J.-L. Ronco, M.O. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_07644442_v333_n2_p81_Loday |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
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. |
| format |
JOUR |
| author |
Loday, J.-L. Ronco, M.O. |
| spellingShingle |
Loday, J.-L. Ronco, M.O. A duality between standard simplices and Stasheff polytopes |
| author_facet |
Loday, J.-L. Ronco, M.O. |
| author_sort |
Loday, J.-L. |
| title |
A duality between standard simplices and Stasheff polytopes |
| title_short |
A duality between standard simplices and Stasheff polytopes |
| title_full |
A duality between standard simplices and Stasheff polytopes |
| title_fullStr |
A duality between standard simplices and Stasheff polytopes |
| title_full_unstemmed |
A duality between standard simplices and Stasheff polytopes |
| title_sort |
duality between standard simplices and stasheff polytopes |
| url |
http://hdl.handle.net/20.500.12110/paper_07644442_v333_n2_p81_Loday |
| work_keys_str_mv |
AT lodayjl adualitybetweenstandardsimplicesandstasheffpolytopes AT roncomo adualitybetweenstandardsimplicesandstasheffpolytopes AT lodayjl dualitybetweenstandardsimplicesandstasheffpolytopes AT roncomo dualitybetweenstandardsimplicesandstasheffpolytopes |
| _version_ |
1807320004257906688 |