Timeline for Modules over Hopf Algebras and $E_2$-algebras
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 11, 2018 at 9:27 | vote | accept | Matthew Levy | ||
| Oct 13, 2018 at 16:15 | comment | added | Pavel Safronov | I believe this is currently being investigated by Costello--Francis--Gwilliam. The $\mathbb{P}_3$-algebra $\mathrm{C}^\bullet(\mathfrak{g})$ is Koszul dual to $\mathrm{U}(\mathfrak{g})$ and the $\mathbb{E}_3$-algebra is Koszul dual to the corresponding quantum group. | |
| Oct 13, 2018 at 13:25 | comment | added | Matthew Levy | Could you tell me a little more about this? (Do you have a reference) I'm primarily interested in knot theory and trying to understand how one can recover quantum knot invariants by procedures similar to this. My advisor thinks the E3 algebra should be something related (quasi-isomorphic) to the E3 deformation complex of U(sl2) (or some other enveloping hopf algebra). Does this sound right? | |
| Oct 13, 2018 at 9:41 | history | edited | YCor | CC BY-SA 4.0 |
added 15 characters in body; edited tags
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| Oct 13, 2018 at 9:15 | comment | added | Pavel Safronov | I couldn't understand the question about $\mathbb{E}_3$. It is indeed true that the $\infty$-category of left modules over an $\mathbb{E}_3$-algebra is braided monoidal. For the Jones polynomial you're looking at the $\mathbb{E}_3$-algebra obtained by quantizing the $\mathbb{P}_3$-algebra $\mathrm{C}^\bullet(\mathfrak{g})$ (the $\mathbb{P}_3$-structure uses the Casimir element on $\mathfrak{g}$). | |
| Oct 13, 2018 at 9:13 | answer | added | Pavel Safronov | timeline score: 6 | |
| Oct 12, 2018 at 23:47 | history | asked | Matthew Levy | CC BY-SA 4.0 |