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3 votes
0 answers
103 views

How to interpret compositional diagrams for quantum sets algebraically

$\newcommand{\id}{\mathrm{id}}$My reference for this post is Musto, Reutter and Verdon's A compositional approach to quantum functions, arXiv:1711.07945. Questions are in bold below. Allow me to begin ...
Ben A-S's user avatar
  • 59
3 votes
1 answer
187 views

Number of Isomorphism Classes of Corepresentations of A Compact Quantum Group

Given a compact quantum group $(G,\Delta)$, with dense Hopf algebra $H$, is it always true that, up to isomorphism, $H$ will have a countable number of irreducible comodules?
Abo Kutis-Felan's user avatar
8 votes
0 answers
488 views

Is there a non-trivial Hopf algebra without left coideal subalgebra?

Let $H$ be a finite dimensional Hopf ${\rm C}^{\star}$-algebra. A $\star$-subalgebra $I$ of $H$ is a left coideal if $\Delta(I) \subset H \otimes I$. $H$ is called maximal if it has no left coideal $\...
Sebastien Palcoux's user avatar
3 votes
0 answers
229 views

The convolution on a semisimple finite quantum groupoid

Let $\mathbb{A}$ be a finite dim. weak Hopf $C^*$-algebra (or semisimple finite quantum groupoid) and $\hat{\mathbb{A}}$ its dual. Let the Fourier transform $\mathcal{F}: \mathbb{A} \to \hat{\mathbb{...
Sebastien Palcoux's user avatar
6 votes
0 answers
239 views

Existence of a Kac algebra for a given fusion ring in a particular class

A $n$-dimensional Kac algebra (i.e., a Hopf C*-algebra), admits finitely many irreducible representations, whose cardinal $r$ is called its rank, the increasing sequence $(d_{1},d_{2},d_{3}, ..., d_{r}...
Sebastien Palcoux's user avatar
2 votes
0 answers
166 views

How simplify the pentagonal equation from two fusion rings?

A semi-simple finite dimensional Hopf algebra $\mathbb{A}$, and its dual $\mathbb{A}^{*}$ produce two fusion categories $\mathcal{C}$ and $\mathcal{C}^{*}$ and then two fusion rings $\mathcal{R}_{1}$ ...
Sebastien Palcoux's user avatar