Structure and Isomorphism Classification of Compact Quantum Groups A_u(Q) and B_u(Q)

Abstract

We classify the compact quantum groups $A_u(Q)$ (resp. $B_u(Q)$) up to isomorphism when $Q>0$ (resp. when $Q\bar{Q}\in \mathbb{R}{I}_n$). We show that the general $A_u(Q)$'s and $B_u(Q)$'s for arbitrary $Q$ have explicit decompositions into free products of these special $A_u(Q)$'s and $B_u(Q)$'s.

arXiv comment13 pages. To appear in Journal of Operator Theory. Details left out in the original version are filled in

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