Q-manifolds and Mackenzie theory: an overview
| dc.creator | Voronov, Theodore | |
| dc.date | 2007-09-26 | |
| dc.date.accessioned | 2026-07-07T08:32:23Z | |
| dc.date.available | 2026-07-07T08:32:23Z | |
| dc.description | This text is meant to be a brief overview of the topics announced in the title and is based on my talk in Vienna (August/September 2007). It does not contain new results (except probably for a remark concerning Q-manifold homology, which I wish to elaborate elsewhere). "Mackenzie theory" stands for the rich circle of notions that have been put forward by Kirill Mackenzie (solo or in collaboration): double structures such as double Lie groupoids and double Lie algebroids, Lie bialgebroids and their doubles, nontrivial dualities for double and multiple vector bundles, etc. "Q-manifolds" are (super)manifolds with a homological vector field, i.e., a self-commuting odd vector field. They may have an extra Z-grading (called weight) not necessarily linked with the Z_2-grading (parity). I discuss double Lie algebroids (discovered by Mackenzie) and explain how this quite complicated fundamental notion is equivalent to a very simple one if the language of Q-manifolds is used. In particular, it shows how the two seemingly different notions of a "Drinfeld double" of a Lie bialgebroid due to Mackenzie and Roytenberg respectively, turn out to be the same thing if properly understood. | |
| dc.description | LaTeX, 17 pages; based on a talk at ESI, August/September 2007 | |
| dc.identifier | https://arxiv.org/abs/0709.4232 | |
| dc.identifier | http://arxiv.org/abs/0709.4232 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138780 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Primary 53D17. Secondary 17B62, 17B66, 18D05, 58A50, 58C50, 58H05 | |
| dc.title | Q-manifolds and Mackenzie theory: an overview | |
| dc.type | text |