Timeline for Actions of two types of Kauffman skein categories
Current License: CC BY-SA 4.0
7 events
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| Dec 17, 2020 at 16:19 | comment | added | David Jordan | It is unfortunately hard to find good references about the above statement, I did find SKEIN RELATIONS AND WILSON LOOPSIN CHERN—SIMONS GAUGE THEORY James H. HORNE, which states the above folklore, although I didn't neatly match the formulas to yours. Perhaps mathscinet search of papers citing that one will yield hits. | |
| Dec 17, 2020 at 16:17 | comment | added | David Jordan | I'm posting this as a comment rather than an answer because I haven't taken the time to investigate the statement fully enough to give a full answer. My understanding is that the Kauffman polynomial captures the SO(N) Chern-Simons invariants in the analogous way that the Homflypt polynomial captures the SU(N) invariants. In particular, I would venture a guess that a certain specialization of your Kauffman case will admit a functor to the subcategory of Rep_q(SL_2) where you have even weights, mapping the monoidal generator to the adjoint rep instead of the defining rep. | |
| Dec 16, 2020 at 21:26 | comment | added | Alistair Savage | Yes, that's probably a more precise formulation of what I'm looking for. I'd like a (nontrivial) functor to the category of modules over some Hopf algebra. | |
| Dec 16, 2020 at 21:21 | comment | added | Noah Snyder | Is your question whether there's some Hopf algebra in the Kauffman case? That is, whether there's some forgetful functor from the Kauffman category to vector spaces? | |
| Dec 16, 2020 at 20:28 | comment | added | Alistair Savage | I understand why the Dubrovnik normalization is the natural one for quantum groups (for the reason you mention). But I'm somehow still unsatisfied that there isn't some nice categorical action (on something else) for the Kauffman normalization. | |
| Dec 16, 2020 at 18:25 | history | edited | Noah Snyder | CC BY-SA 4.0 |
added 240 characters in body
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| Dec 16, 2020 at 18:06 | history | answered | Noah Snyder | CC BY-SA 4.0 |