Complexity and module varieties for classical Lie superalgebras
| dc.creator | Boe, Brian D. | |
| dc.creator | Kujawa, Jonathan R. | |
| dc.creator | Nakano, Daniel K. | |
| dc.date | 2009-05-14 | |
| dc.date.accessioned | 2026-07-07T13:15:06Z | |
| dc.date.available | 2026-07-07T13:15:06Z | |
| dc.description | Let g=g_{0} \oplus g_{1} be a classical Lie superalgebra and F be the category of finite dimensional g-supermodules which are semisimple over g_{0}. In this paper we investigate the homological properties of the category F. In particular we prove that F is self-injective in the sense that all projective supermodules are injective. We also show that all supermodules in F admit a projective resolution with polynomial rate of growth and, hence, one can study complexity in F. If g is a Type I Lie superalgebra we introduce support varieties which detect projectivity and are related to the associated varieties of Duflo and Serganova. If in addition g has a (strong) duality then we prove that the conditions of being tilting or projective are equivalent. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/0905.2403 | |
| dc.identifier | http://arxiv.org/abs/0905.2403 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230382 | |
| dc.subject | Representation Theory | |
| dc.subject | 17B56, 17B10; 13A50. | |
| dc.title | Complexity and module varieties for classical Lie superalgebras | |
| dc.type | text |