Timeline for tensor hierarchy for Lie groups from Maurer-Cartan form
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 7, 2013 at 17:33 | vote | accept | John | ||
| Aug 7, 2013 at 17:33 | vote | accept | John | ||
| Aug 7, 2013 at 17:33 | |||||
| Aug 7, 2013 at 7:20 | vote | accept | John | ||
| Aug 7, 2013 at 17:33 | |||||
| Aug 6, 2013 at 19:55 | answer | added | Peter Michor | timeline score: 3 | |
| Aug 6, 2013 at 14:13 | comment | added | John | Indeed, the question is vague and a lot was put on 'nice Lie group term'. My interest is in higher rank tensors one can have and I will accept any Lie group that is needed for them to exists. | |
| Aug 6, 2013 at 13:55 | answer | added | Ben McKay | timeline score: 5 | |
| Aug 6, 2013 at 9:36 | comment | added | Robert Bryant | Hmmm. You have some confusion here, and I'm not sure exactly what you mean by 'make the covariant index...explicit'. However, you should know that, if you just take any basis of left-invariant forms, then the formula you wrote down for a metric $g$ will not be bi-invariant. (In fact, many Lie groups do not even admit a bi-invariant volume form, let alone a metric, so you will need to say what you mean by 'nice', too.) The bi-invariant tensors on a given Lie group are controlled by its adjoint representation, and that gives the whole story there. Yes, these have lots of applications. | |
| Aug 5, 2013 at 23:35 | history | edited | John | CC BY-SA 3.0 |
added 5 characters in body
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| Aug 5, 2013 at 23:19 | history | asked | John | CC BY-SA 3.0 |