Timeline for About enveloping algebras of direct sums
Current License: CC BY-SA 4.0
24 events
| when toggle format | what | by | license | comment | |
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| May 5 at 9:25 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
Added a missing bracket
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| May 3 at 21:24 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
Gave the reference to a complete and general solution.
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| Apr 25, 2023 at 19:46 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
Changed some bold font to be less assertive
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| Oct 29, 2022 at 21:45 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
Added the word "an" [as answer] ---> [as an answer]
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| Oct 29, 2022 at 21:34 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
Changed proof ---> tentative proof
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| Jul 8, 2018 at 6:00 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
Added remark (i)
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| Jun 18, 2018 at 20:16 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
fixed errors
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| Jun 10, 2018 at 8:23 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
fixed an error
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| Jun 10, 2018 at 6:02 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
added Proof of $\mathcal{J}_{11}\subset ker(\beta_0)$
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| Jun 10, 2018 at 4:50 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
added remarks about finite and infinite decompositions
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| Jun 9, 2018 at 22:43 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
Proof of identity (*)
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| Jun 9, 2018 at 22:34 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
Proof of identity (*)
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| Jun 9, 2018 at 22:09 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
labelling identity (*)
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| Jun 9, 2018 at 21:50 | comment | added | darij grinberg | OK, I admit I don't understand how you prove the "last identity" either. | |
| Jun 9, 2018 at 21:48 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
fixed typos
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| Jun 9, 2018 at 21:21 | comment | added | Duchamp Gérard H. E. | @darijgrinberg [But I don't quite see how you get ...]---> One has $\ker(\rho)\subset \ker(\beta_0)$ then, due to the last identity $$\beta_0(u\otimes B(g_1,h_1)\otimes v)=\beta_0(u_1\otimes B(g_1,h_1)\otimes u_2)=0$$ where $u_i\in T(\mathfrak{g}_i)$ | |
| Jun 9, 2018 at 21:12 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
fixed indices and made precise the domains of g_2 et h_1
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| Jun 9, 2018 at 20:41 | comment | added | darij grinberg | Also, it might be that you don't need the AAU structure any more, since the fact that $\ker \rho$ is an ideal follows straight from property 4. Unless you tacitly use it in the proof of $\mathcal{J}_{11} \subseteq \ker\beta_0$ (is $s_1 \otimes s_2$ an algebra homomorphism?). | |
| Jun 9, 2018 at 20:39 | comment | added | darij grinberg | This is looking better and better! But I don't quite see how you get $\mathcal{J}_{11} \subseteq \ker\beta_0$. Also, minor typo: one of the $\mathcal{U}(\mathfrak{g})$s in the commutative diagram should be a $\mathcal{U}(\mathfrak{g}_1)$. | |
| Jun 9, 2018 at 19:06 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
unfolded associativity
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| Jun 9, 2018 at 17:38 | comment | added | darij grinberg | Let me know when you've fixed the associativity argument (or maybe you don't need it?). BTW: If you can show the analogous fact for an arbitrary direct sum (not just of $2$ submodules), then you'll have gotten a new proof of Poincaré-Birkhoff-Witt (even one of the more general versions: the one where $\mathfrak{g}$ is assumed to be a direct sum of cyclic modules). | |
| Jun 9, 2018 at 17:23 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
removed typos and formatting
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| Jun 9, 2018 at 17:18 | comment | added | darij grinberg | Why is the multiplication $*$ associative? Also, some extraneous $\in$ signs in the definition of $r_{w,i}$. | |
| Jun 9, 2018 at 16:58 | history | answered | Duchamp Gérard H. E. | CC BY-SA 4.0 |