2
votes
1answer
93 views

What is the multiplicative unitary for SU_q(2) (or other quantum groups)?

Consider a (von Neumann algebraic) locally compact quantum group $(M, \Delta, \phi, \psi)$ where the von Neumann algebra $M$ is realized as operators on the Hilbert space $H$. There is a ...
3
votes
0answers
77 views

States and extremal states of quantum SU(2) and the Podleś sphere

Is there any description (preferably somehow related to the original generators) for the state space (as in C*-algebras) of quantum SU(2) and the Podleś sphere? If so (this is pushing my luck) are the ...
3
votes
0answers
110 views

How a unitary corepresentation of a Hopf C*-algebra, deals with the antipode?

Let $\mathcal{A}$ be a Kac algebra (Hopf C*-algebra), with comultiplication $\delta$, counit $\epsilon$ and antipode $S$. The following definition comes from this paper (p51-52) of ...
3
votes
1answer
152 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 ...
11
votes
1answer
480 views

A left inverse for the comultiplication on a Hopf von Neumann algebra

Edit: incorrect claim at end of earlier version; thanks to Matthew Daws for pointing this out in comments. $\newcommand{\cM}{{\mathcal M}}\newcommand{\stp}{{\overline{\otimes}}}$The following ...
7
votes
0answers
280 views

Quantum Braid Group

Recently I learned the definition of the quantum permutation group $A_s(n)$, which starts from the fundamental representation by permutation matrices and exchanges the entries by noncommuting ...
6
votes
4answers
927 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 ...