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Results tagged with qa.quantum-algebra
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user 13767
Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
4
votes
0
answers
88
views
Are there any dominant pivotal functors such that the regular representation is not mapped o...
This question is related to Pivotal functors of that are substantially different from finite group homomorphisms.
A tensor functor $F: \mathcal{C} \to \mathcal{D}$ is called dominant (sometimes calle …
- 5,565
1
vote
Do all 3D TQFTs come from Reshetikhin-Turaev?
If your TQFT does not extend to the circle, (EDIT: and you're willing to generalise to lax TQFTs,) then the answer is no. A reference is: https://arxiv.org/abs/1408.0668
The proof goes by an explicit …
- 5,565
10
votes
0
answers
285
views
What's the relation between half-twists, star structures and bar involutions on Hopf algebras?
A star structure on a Hopf algebra is an antilinear antiautomorphism squaring to 1 and satisfying some further axioms. A Hopf algebra with a star structure is then a star algebra and a Hopf algebra in …
- 5,565
6
votes
2
answers
280
views
When are the braid relations in a quasitriangular Hopf algebra equivalent?
Quasitriangular Hopf algebras have to satisfy, amongst other conditions, the following equations:
$$(\Delta \otimes \mathrm{id}) (R) = R_{13} R_{23}$$
$$(\mathrm{id} \otimes \Delta) (R) = R_{13} R_{12 …
- 5,565