Timeline for Difference between the Laplacian and the sub-Laplacian of a Lie group
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 2, 2016 at 23:00 | vote | accept | Z. Alfata | ||
| S Apr 2, 2016 at 14:07 | history | suggested | Raziel |
added tag sub-riemannian (more appropriate than harmonic analysis)
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| Apr 2, 2016 at 13:49 | review | Suggested edits | |||
| S Apr 2, 2016 at 14:07 | |||||
| Apr 2, 2016 at 13:12 | answer | added | Raziel | timeline score: 8 | |
| Apr 2, 2016 at 12:54 | comment | added | Ben McKay | If you use two translation invariant Riemannian metrics on Euclidean space, you can already get quite a mess as the difference between their Laplace operators: elliptic, hyperbolic, or neither. So I think you need to make some special choice of which metric you use, and also which $G$-invariant subbundle to give your sub-Laplacian. This question would benefit from some thought about which operators you have in mind, since a Lie group does not have a single choice of Laplace operator or sub-Laplace operator. | |
| Apr 2, 2016 at 11:01 | comment | added | Sebastian Goette | The sub-Laplacian depends on some extra structure, doesn't it? On the Heisenberg group, there might be a most natural choice, but what about other Lie groups? From your example, one might expect to obtain a Riemannian submersion $G\to G/H$ whose horizontal fields generate the Lie algebra of all vector fields, and the difference operator would be the fibrewise Laplacian. But this seems to use a nice correlation between the Riemannian metric on $G$ and the Lie algebra structure. | |
| Apr 2, 2016 at 10:39 | history | edited | Stefan Kohl♦ | CC BY-SA 3.0 |
Likely 'difference' is meant rather than 'deference'.
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| Apr 2, 2016 at 10:21 | history | rollback | Z. Alfata |
Rollback to Revision 1
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| Apr 2, 2016 at 10:15 | history | edited | Ben McKay | CC BY-SA 3.0 |
spelling
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| Apr 2, 2016 at 10:08 | history | asked | Z. Alfata | CC BY-SA 3.0 |