Timeline for Quantum groups and deformations of the monoidal category of $U(\frak{g})$-modules
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 4, 2018 at 9:57 | comment | added | Adrien | Note that while "being modules for an Hopf algebra" is an extra structure while "being modules for a quasi-Hopf algebra" is a property, which I think is preserved under formal deformations under reasonable assumptions... | |
| Nov 4, 2018 at 9:12 | comment | added | Adrien | @NoahSnyder Drinfeld's paper deals with twist-equivalence classes of deformations of $U(\mathfrak g)$ as a (quasi-triangular-)quasi-Hopf algebra, so you're right it's not entirely obvious that it also classifies deformations as (braided) tensor categories, but I think at least for semi-simple $\mathfrak g$ this is the case. | |
| Nov 4, 2018 at 8:55 | comment | added | Adrien | @VictorProtsak RIght, of course, I edited. | |
| Nov 4, 2018 at 8:55 | history | edited | Adrien | CC BY-SA 4.0 |
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| Nov 4, 2018 at 5:08 | comment | added | Victor Protsak | If $\mathfrak{g}$ is a semisimple Lie algebra with $k$ simple components then the space of invariant symmetric bilinear forms is $k$-dimensional, and the same is true for invariant symmetric 2-tensors. (One can independently rescale the Killing form on each component by its own scalar.) | |
| Nov 3, 2018 at 22:18 | comment | added | Noah Snyder | Is this really deformations of the tensor category, or just of the Hopf algebra? | |
| Nov 3, 2018 at 18:48 | history | edited | Adrien | CC BY-SA 4.0 |
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| Nov 3, 2018 at 18:33 | history | answered | Adrien | CC BY-SA 4.0 |