Finite Dimensionality of Irreducible Unitary Representations of Compact Quantum Groups

Abstract

In this paper, we study the representations of Hopf ${C^ \ast }$-algebras; the main result is that every irreducible left unitary representation of a Hopf ${C^\ast }$-algebra with a Haar measure is finite dimensional. To prove this result, we first study the comodule structure of the space of Hilbert-Schmidt operators; then we use this comodule structure to show that every irreducible left unitary representation of a Hopf ${C^\ast }$-algebra with a Haar measure is finite dimensional.

Locations

• Proceedings of the American Mathematical Society - View - PDF