Timeline for Invariant proof that De Rham differential is a derivation?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Mar 18, 2021 at 0:30 | comment | added | Martin Gisser | I always wondered about the crazy shuffle formula for \wedge. Why? This doesn't look like Hopf algebra (The shuffle comultiplication is very important and fundamental)... | |
| S Dec 31, 2017 at 2:04 | history | suggested | Arctic Char | CC BY-SA 3.0 |
add corresponding link in MSE
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| Dec 31, 2017 at 1:24 | review | Suggested edits | |||
| S Dec 31, 2017 at 2:04 | |||||
| Dec 30, 2017 at 10:11 | comment | added | Hu xiyu | Why do not directly calculate under a basis with the given property of $\wedge$ and $d$? | |
| Dec 30, 2017 at 0:31 | comment | added | Peter Michor | See page 119ff of mat.univie.ac.at/~michor/dgbook.pdf. | |
| Dec 29, 2017 at 18:04 | history | edited | PtF | CC BY-SA 3.0 |
deleted 776 characters in body
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| Dec 29, 2017 at 18:03 | comment | added | PtF | The problem boils down to establishing the bijections$\mathsf{Sh}(1, p+q)\times \mathsf{Sh}(p, q)\simeq \mathsf{Sh}(p+1, q)\times \mathsf{Sh}(1, p)$ and $\mathsf{Sh}(1, p+q)\times \mathsf{Sh}(p, q)\simeq \mathsf{Sh}(p, q+1)\times \mathsf{Sh}(1, q)$ and this really. | |
| Dec 29, 2017 at 14:35 | comment | added | PtF | @DeaneYang maybe, I'll give it a try, thanks for the hint =) | |
| Dec 29, 2017 at 11:14 | comment | added | Sebastian Goette | I guess one can write a rather tedious direct proof, starting from the observation that in the first term of the definition of $d$, $X_{\sigma(1)}$ either differentiates the first or the second factor (because it is a derivation). And in the second term, inserting the commutator happens in the first or in the second factor (because inserting a vector field is a derivation, too). Grouping the terms in $d(\varepsilon\wedge\eta)$ correspondingly should prove the claim. | |
| Dec 29, 2017 at 5:33 | comment | added | Deane Yang | Also, isn't it easier to write everything in terms of the full symmetric group instead of shuffles? | |
| Dec 29, 2017 at 1:01 | comment | added | Bernie | Have you tried induction on degrees? | |
| Dec 29, 2017 at 0:50 | history | asked | PtF | CC BY-SA 3.0 |