Timeline for connections on AN(3) Lie group
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 27, 2010 at 0:55 | answer | added | Richard Montgomery | timeline score: 2 | |
| Nov 26, 2010 at 17:25 | comment | added | José Figueroa-O'Farrill | I guess the question is what you mean by 'natural'. On homogeneous spaces (of which Lie groups are of course examples) there is a notion of invariant connection, as described in, say, Kobayashi-Nomizu. Another possible notion of 'natural' connection would be the Levi-Civita connection of some left-invariant metric. | |
| Nov 26, 2010 at 16:57 | comment | added | Jerzy Kowalski-Glikman | You can find the explicit representation of the algebra and group in our paper arXiv:0706.3658 [hep-th] (section IIA). From there you can also easily reconstruct the metric and Levi-Civita connection. The metric turns out to be $-dt^2 +e^t\, \sum (dx^i)^2$ | |
| Nov 26, 2010 at 15:48 | comment | added | Deane Yang | I don't know what AN(3) is; do you have a more concrete description of the group itself and not just its Lie algebra? How do you imbed it in $R^5$? Finally, your description of how you construct the Levi-Civita connection is rather vague and does not sound natural to me. Could you provide more detail on that? | |
| Nov 26, 2010 at 11:18 | comment | added | Jerzy Kowalski-Glikman | Sure, but I can imbed it in $R^5$ and use the induced metric. | |
| Nov 26, 2010 at 9:05 | comment | added | Guillaume Brunerie | “The AN(3) group is a 4-dimensional manifold, so I can clearly construct a Levi-Civita connection on it (with non-zero curvature and zero torsion).” Well, you need a riemannian metric on it in order to have a Levi-Civita connection. | |
| Nov 26, 2010 at 8:36 | history | asked | Jerzy Kowalski-Glikman | CC BY-SA 2.5 |