Timeline for When is the exterior derivation $d$ a Lie algebra morphism?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Jul 8, 2020 at 0:58 | vote | accept | Ali Taghavi | ||
| S Jul 7, 2020 at 14:10 | history | bounty ended | Ali Taghavi | ||
| S Jul 7, 2020 at 14:10 | history | notice removed | Ali Taghavi | ||
| Jul 6, 2020 at 23:56 | answer | added | Joel Villatoro | timeline score: 3 | |
| S Jun 30, 2020 at 17:54 | history | bounty started | Ali Taghavi | ||
| S Jun 30, 2020 at 17:54 | history | notice added | Ali Taghavi | Draw attention | |
| Jun 28, 2020 at 13:04 | comment | added | Ali Taghavi | @PaulReynolds Thank you very much for informing me of this graded bracket. | |
| Jun 28, 2020 at 7:46 | comment | added | Ali Taghavi | @BK Thank you very much for your interesting comment. Could you please more explain about its last part?(About the contradiction you pointed out) | |
| Jun 25, 2020 at 21:59 | comment | added | Paul Reynolds | I feel like it's more natural to use the Schouten–Nijenhuis bracket on higher degree forms (along with the symplectic form vector-covector identification), rather than a plain Lie bracket. | |
| Jun 25, 2020 at 21:38 | comment | added | B K | On Question 1: The Poisson bracket (or its negative, depending on the sign convention) has the property that $d:\Omega^0(M)\to \Omega^1(M)$ becomes a Lie algebra morphism if $\Omega^1(M)$ is identified with the space of smooth vector fields $\chi^\infty(M)$ using the symplectic form. No need for a Riemannian metric here. I even doubt that there can exist one as in the question, as such a metric would probably have to induce the same isomorphism from $\Omega^1(M)$ to $\chi^\infty(M)$ as the symplectic form, which would make it an antisymmetric tensor, a contradiction. | |
| Jun 25, 2020 at 19:36 | history | edited | LSpice | CC BY-SA 4.0 |
Proofreading
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| Jun 25, 2020 at 19:19 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Jun 25, 2020 at 19:12 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
added 20 characters in body; edited tags
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| Jun 25, 2020 at 19:04 | history | asked | Ali Taghavi | CC BY-SA 4.0 |