Skip to main content

All Questions

Filter by
Sorted by
Tagged with
9 votes
1 answer
207 views

Separability of compact quantum groups

In the theory of compact quantum groups due Woronowicz, we assume usually that the C*-algebra of the compact quantum group is separable. Is the assumption essential in the theory? Will it eventually ...
Marie Anderlecht's user avatar
9 votes
0 answers
268 views

Existence/characterization/properties of $C^*$-algebras which "are" quantization of compact symplectic manifolds?

Understanding of "quantization" achieved much progress recent years, especially after Kontsevich breakthrough on deformation quantization, where he proved one-to-one correspondence between Poisson ...
Alexander Chervov's user avatar
8 votes
1 answer
483 views

Eigenvalues of the free sphere

Consider the usual sphere $S^{n-1}\subset\mathbb R^n$. By Stone-Weierstrass $C(S^{n-1})$ is generated by the standard coordinates $x_1,\ldots,x_n:\mathbb R^n\to\mathbb R$, and in fact we have the ...
Richard's user avatar
  • 1,363
7 votes
4 answers
1k views

Compact Quantum Groups from Hopf Algebras

For a compact quantum group $C_q[G]$, it was shown by Woronowicz that $C_q[G]$ contains a dense Hopf algebra generalising the algebra of representations of $G$. I am interested in the other way around,...
John McCarthy's user avatar
5 votes
1 answer
228 views

Zero divisors in compact quantum groups

Let $\mathcal{G}$ be compact quantum group in the sense of S. L. Woronowicz. As is well-known, every compact quantum group contains a dense Hopf algebra, called the polynomial Hopf algebra Pol$(\...
Dave Shulman's user avatar
4 votes
1 answer
275 views

What are the norms of the generators of the standard Podleś sphere?

Fix a real number $0<q<1$. We consider the standard Podles sphere $A_q$ as the universal unit $C^*$-algebra generated by $a$ and $b$ with relations \begin{equation*} \begin{split} &a=a^*,~ ...
Zhaoting Wei's user avatar
  • 9,019
4 votes
0 answers
338 views

Quantization of $S^2$ as $C^*$-algebra?

The general context for the question - is belief that quantization of compact symplectic manifolds can be endowed with the structure of $C^*$-algebra (see MO230695). The particular question is about ...
Alexander Chervov's user avatar
3 votes
1 answer
248 views

example of a compact quantum group at a root of unity?

In Woronowicz's theory of compact quantum groups, the most well-known example is $SU_q(2)$, for $q$ a real number. Moreover, all the other examples of compact quantum groups, based some Drinfeld--...
Mike Owen's user avatar
0 votes
1 answer
144 views

Is a NC sphere a (one point) compactification of a NC plane?

Inspired by this question About noncommutative sphere and inspired by the fact that the classical sphere is the one point compactificatiin of $\mathbb{R}^2$ we ask the question below: Is the non ...
Ali Taghavi's user avatar