Superpotentials and Higher Order Derivations
| dc.creator | Bocklandt, Raf | |
| dc.creator | Schedler, Travis | |
| dc.creator | Wemyss, Michael | |
| dc.date | 2008-02-01 | |
| dc.date | 2008-05-12 | |
| dc.date.accessioned | 2026-07-07T09:37:56Z | |
| dc.date.available | 2026-07-07T09:37:56Z | |
| dc.description | We consider algebras defined from quivers with relations that are k-th order derivations of a superpotential, generalizing results of Dubois-Violette to the quiver case. We give a construction compatible with Morita equivalence, and show that many important algebras arise in this way, including McKay correspondence algebras for GL_n for all n, and four-dimensional Sklyanin algebras. More generally, we show that any N-Koszul, (twisted) Calabi-Yau algebra must have a (twisted) superpotential, and construct its minimal resolution in terms of derivations of the (twisted) superpotential. This yields an equivalence between N-Koszul twisted Calabi-Yau algebras A and algebras defined by a superpotential such that an associated complex is a bimodule resolution of A. Finally, we apply these results to give a description of the moduli space of four-dimensional Sklyanin algebras using the Weil representation of SL_2(Z/4). | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/0802.0162 | |
| dc.identifier | http://arxiv.org/abs/0802.0162 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160632 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16E65 | |
| dc.title | Superpotentials and Higher Order Derivations | |
| dc.type | text |