# Journal of Operator Theory

Volume 48, Issue 3, Supplementary 2002 pp. 573-583.

Structure and isomorphism classification of $A_{\rm u}(Q)$ and $B_{\rm u}(Q)$**Authors**: Shuzhou Wang

**Author institution:**Department of Mathematics, University of Georgia, Athens, GA 30602, Georgia

**Summary:**We classify the compact quantum groups $A_{\rm u}(Q)$ (respectively, $B_{\rm u}(Q)$) up to isomorphism when $Q>0$ (respectively, when $Q \bar{Q} \in {\bbb R} I_n$). We show that the general $A_{\rm u}(Q)$'s and $B_{\rm u}(Q)$'s for arbitrary $Q$ have explicit decompositions into free products of these special $A_{\rm u}(Q)$'s and $B_{\rm u}(Q)$'s.

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