The small quantum group and the Springer resolution
| dc.creator | Bezrukavnikov, Roman | |
| dc.creator | Lachowska, Anna | |
| dc.date | 2006-09-28 | |
| dc.date | 2007-01-29 | |
| dc.date.accessioned | 2026-07-07T07:43:18Z | |
| dc.date.available | 2026-07-07T07:43:18Z | |
| dc.description | In math.RT/0304173 the derived category of the principal block in modules over the Lusztig quantum algebra at a root of unity is related to the derived category of equivariant coherent sheaves on the Springer resolution. In the present paper we deduce a similar relation between the derived category of the principal block for the {\em small (reduced) quantum algebra} and the derived category of (non-equivariant) coherent sheaves on the Springer resolution. As an application we get a geometric description of Hochschild cohomology (in particular, the center) of the regular block for the small quantum group, and use it to give an explicit description of a certain subalgebra in the center (obtained previously by another method and under more restrictive assumptions in math.QA/0107098. We also briefly explain the relation of our result to the geometric description math.RT/0407048 of the derived category of modules over the De Concini -- Kac quantum algebra. | |
| dc.description | MPIM preprint, to appear in Proceedings of Haifa Conference on Quantum Groups; the second version contains minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0609819 | |
| dc.identifier | http://arxiv.org/abs/math/0609819 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122771 | |
| dc.subject | Representation Theory | |
| dc.title | The small quantum group and the Springer resolution | |
| dc.type | text |