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9 votes
1 answer
585 views

Finite compact quantum groups

Let $(A, \Delta)$ be a $C^*$-algebraic compact quantum group (in the sense of Woronowicz). It is called finite if $A$ is a finite-dimensional $C^*$-algebra. By elementary $C^*$-algebra theory, we ...
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
5 votes
1 answer
202 views

Relating different constructions of the universal compact quantum group

Before asking my question, let me give the necessary background. Readers that are comfortable with the language of universal and reduced compact quantum groups may skip the following two sections. ...
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5 votes
1 answer
283 views

Reference request quantum SU(3)

Woronowicz shows that the C*-algebras of quantum $SU(2)$ are isomorphic (only as C*-algebras, forgetting the quantum group structure). Are there similar results for quantum $SU(n)$ for $n \geq 3$?
Clipper Gomberg'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
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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
2 votes
2 answers
217 views

Kernel of intertwiner is invariant (compact quantum groups)

Before asking my question, let me introduce the relevant terminology. Throughout, let $(A, \Delta)$ be a compact quantum group. Definition: A representation $v$ on the Hilbert space $H$ is an element $...
user avatar
0 votes
1 answer
261 views

Definition intertwiner of representations of compact quantum groups

Before asking my question, let me introduce the relevant terminology. Throughout, let $(A, \Delta)$ be a compact quantum group. Definition: A representation $v$ on the Hilbert space $H$ is an element $...
user avatar
0 votes
1 answer
158 views

Showing a product on a character space is continuous

Quoting from Timmermann's An invitation to quantum groups and duality: Prop. 5.1.3 Let $A$ be a commutative algebra of functions on a compact quantum group. Then there exists a compact group $G$ and ...
JP McCarthy's user avatar
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