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A noncommutative 2-sphere generated by the quantum complex plane

Ismael Cohen, Elmar Wagner (2012)

Banach Center Publications

S. L. Woronowicz's theory of C*-algebras generated by unbounded elements is applied to q-normal operators satisfying the defining relation of the quantum complex plane. The unique non-degenerate C*-algebra of bounded operators generated by a q-normal operator is computed and an abstract description is given by using crossed product algebras. If the spectrum of the modulus of the q-normal operator is the positive half line, this C*-algebra will be considered as the algebra of continuous functions...

A Note on Free Quantum Groups

Teodor Banica (2008)

Annales mathématiques Blaise Pascal

We study the free complexification operation for compact quantum groups, G G c . We prove that, with suitable definitions, this induces a one-to-one correspondence between free orthogonal quantum groups of infinite level, and free unitary quantum groups satisfying G = G c .

Actions of monoidally equivalent compact quantum groups and applications to probabilistic boundaries

An De Rijdt, Nikolas Vander Vennet (2010)

Annales de l’institut Fourier

The notion of monoidal equivalence for compact quantum groups was recently introduced by Bichon, De Rijdt and Vaes. In this paper we prove that there is a natural bijective correspondence between actions of monoidally equivalent quantum groups on unital C * -algebras or on von Neumann algebras. This correspondence turns out to be very useful to obtain the behavior of Poisson and Martin boundaries under monoidal equivalence of quantum groups. Finally, we apply these results to identify the Poisson boundary...

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