The Operad Quad is Koszul
| dc.creator | Vatne, Jon Eivind | |
| dc.date | 2004-11-25 | |
| dc.date | 2005-03-30 | |
| dc.date.accessioned | 2026-07-07T05:14:42Z | |
| dc.date.available | 2026-07-07T05:14:42Z | |
| dc.description | The purpose of this paper is to prove the koszulity of the operad ${\mathcal Quad}$, governing quadri-algebras. That ${\mathcal Quad}$ is Koszul was conjectured by Aguiar and Loday. The operad ${\mathcal Dend}$, governing dendriform algebras, is known to be Koszul, by work of Loday, and ${\mathcal Quad}$ is its second black square power. We find a new complex, based on the associahedron, which captures the structure of ${\mathcal Dend}$. This complex behaves well with respect to the black squaring process, and allows us to conclude. Also, this proves koszulity of higher powers of ${\mathcal Dend}$. | |
| dc.description | 14 pages; exposition clarified, notation updated and typos corrected | |
| dc.identifier | https://arxiv.org/abs/math/0411580 | |
| dc.identifier | http://arxiv.org/abs/math/0411580 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73378 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Rings and Algebras | |
| dc.title | The Operad Quad is Koszul | |
| dc.type | text |