Anti-deformation conjecture for Woronowicz algebras

A Woronowicz algebra is a compact quantum-group $C^*$-algebra, and a Woronowicz-Kac algebra is a finitely generated Woronowicz algebra whose antipode is involutive. An $R^+$-deformation preserves the fusion semiring $R^+$, and it is dimension-preserving when corresponding corepresentations have the same dimensions.

Anti-deformation conjecture. Any Woronowicz algebra is a dimension-preserving $R^+$-deformation of a Woronowicz-Kac algebra.

The claim reflects the observation that the known non-Kac examples arise mainly from positive $q$-deformations and related constructions, while many operator-algebraic applications use Kac-type quantum groups. The source presents the relationship as conjectural and does not establish it in general.