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I think you can find more in Lieb and Seiringer's book "The Stability of Matter in Quantum Mechanics", or see also Freeman Dyson http://www.webofstories.com/play/4415 and the book review http://arxiv. …

Hartmut Fuehr's book (Abstract harmonic analysis of continuous wavelet transforms, Springer Lecture Notes in Mathematics, Nr. 1863, 2005, X, 193 p., Softcover ISBN: 3-540-24259-7), contains a "-reaso …

Non-degenerate *-homorphism from $A$ (or $M(A)$) to $M(B)$ are strict (where non-degenerate means that $\phi(A)B$ is total in $B$). An important property of strict maps $\phi:A\to M(B)$ is that they …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

There have been many attempts to develop a mathematical theory of quantisation, a functor that produces a quantum system for a given classical (Hamiltonian) system. Ideally, one would like to replace …

I am looking for a a description of the algebra of continuous central functions on a group, say a compact simple Lie group $G$, as the algebra of all continuous functions on a "nice" compact Hausdorff …