Residually finite quantum group algebras
Abstract
We show that provided $n\ne 3$, the involutive Hopf *-algebra $A_u(n)$ coacting universally on an $n$-dimensional Hilbert space has enough finite-dimensional representations in the sense that every non-zero element acts non-trivially in some finite-dimensional *-representation. This implies that the discrete quantum group with group algebra $A_u(n)$ is maximal almost periodic (i.e. it embeds in its quantum Bohr compactification), answering a question posed by P. So tan. We also prove analogous results for the involutive Hopf *-algebra $B_u(n)$ coacting universally on an $n$-dimensional Hilbert space equipped with a non-degenerate bilinear form.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2014
- DOI:
- 10.48550/arXiv.1410.1215
- arXiv:
- arXiv:1410.1215
- Bibcode:
- 2014arXiv1410.1215C
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematics - Operator Algebras;
- Mathematics - Rings and Algebras;
- 16T05;
- 16T20;
- 46L52
- E-Print:
- 17 pages + references