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arXiv · funct-an/9302006

On the Fock representation of the q-commutation relations

Ken Dykema·Alexandru Nica
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Abstract

The q-commutation relations in the title are those that have recently received much attention, and that for -1<q<1 provide an interpolation between Bosonic and Fermionic statistics, passing through free statistics at q=0. We look at the C*-algebra R^q generated by the representation of these relations on the twisted Fock space of Bozejko-Speicher, and we find a canonical unitary U_q from the twisted Fock space to usual full Fock space, such that U_q R^q (U_q)^* contains the Cuntz algebra R^0, and such that we have equality for |q|<0.44.

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Ken Dykema, Alexandru Nica. 1993-02-22. On the Fock representation of the q-commutation relations. https://arxiv.org/abs/funct-an/9302006

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