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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