Characterization of compact quantum group

Abstract

Given a C^*-algebra A and a comultiplication Φ on A, we show that the pair (A,Φ) is a compact quantum group if and only if the associated multiplier Hopf *-algebra (A,{\mathrm{\Phi }}_A) is a compact Hopf *-algebra.

Keywords

Compact quantum group / associated multiplier Hopf *-algebra / compact Hopf *-algebra

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Higher Education Press and Springer-Verlag Berlin Heidelberg