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Results tagged with qa.quantum-algebra
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user 30364
Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
13
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7
answers
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views
Open problems in the theory of compact quantum groups
What are the important open problems in the theory of compact quantum groups? Or conjectures?
Here is an example from An De Rijdt's Ph.D. thesis: Is every compact quantum group with the fusion rules …
10
votes
Accepted
Eigenvalues of the free sphere
How about
$\lambda_k = \frac{U'_k(n)}{U_k(n)}$
where the $U_k$ denote the Chebyshev polynomials of the second kind, $U_0(x)=1$, $U_1(x)=x$, and $U_k(x)=xU_{k-1}(x)-U_{k-2}(x)$ for $k\ge 2$.
In Sect …
- 2,201
8
votes
expository papers related to quantum groups
Don't forget the "classics" on compact quantum groups:
Woronowicz, S.L., Compact quantum groups. Symétries quantiques (Les Houches, 1995), 845–884, North-Holland, Amsterdam, 1998.
See also http://ww …
- 2,201
7
votes
Compact Quantum Groups from Hopf Algebras
A little side remark, concerning the last part of your question: Marc Rosso describes in
Marc Ross, Algèbres enveloppantes quantifiées, groupes quantiques compacts de matrices et calcul différentiel …
- 2,201
5
votes
Open problems in the theory of compact quantum groups
An De Rijdt describes another open problem in her thesis, see the summary of Chapter 3 on page 2: The study of ergodic action of compact quantum groups. Here we have the results of Wassermann for comp …
5
votes
What is quantum Brownian motion?
No answer, just another question:
Is quantum Brownian motion related to Quantum Noise or the quantum Wiener process? I think these notions have a well-established mathematical theory, e.g. there are …
- 2,201
4
votes
Open problems in the theory of compact quantum groups
Questions concerning coamenability
Here are few more open questions :
a) Reiji Tomatsu stated in
Reiji Tomatsu, Amenable discrete quantum groups, Journal of the Mathematical Society of Japan
Vol. 5 …
4
votes
Open problems in the theory of compact quantum groups
Links to few questions that have already been published on MO:
a) Why is the quantum Lorentz group not connected?
Or: What does it mean for a a (compact) quantum group to be connected? (Ok, the (quan …
4
votes
Open problems in the theory of compact quantum groups
I found another open CQG problem on MO, there is even a reward of 3 bottles of champagne offered for solving it:
J.-B. Zuber offered respectively 1, 2 and 3 bottles of Champagne for the classifica …
3
votes
Accepted
Real forms of Drinfeld-Jimbo quantum groups
Two references I recall are
E. Twietmeyer, Real forms of Uq (g), Lett. Math. Phys. 24, 49-58, 1992.
V. Lyubashenko, Real and imaginary forms of quantum groups, Lecture Notes in Math. 1510, 1992, pp …
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2
votes
Open problems in the theory of compact quantum groups
Maybe the study (and explicite computation) of the 6j-Symbols/Wigner-Racah coefficients can also be considered as a problem in the theory of compact quantum groups... see
Calculating 6j-symbols (aka …