q-canonical commutation relations and stability of the Cuntz algebra

verfasst von

P. E. T. Jo rgensen, L. M. Schmitt, R. F. Werner

Abstract

We consider the q-deformed canonical commutation relationslbreak asb i a- q aasb i= deltaij1, i, j = 1, ..., d, where d is an integer and - 1 lt q . We show the existence of a universal solution of these relations, realized in a C*-algebra E this algebra is the Cuntz algebra extended by an ideal isomorphic to the compact operators, also known as the Cuntz-Toeplitz algebra. We show that for a general class of commutation relations of the form asb i a = Gammaij(a,..., a with GammaToeplitz algebra. For the particular case of the q-canonical commutation relations this result applies for q lt - 1. Hence for these values Esb q is isomorphic to E. The example asb i a - qa asb j= deltaij1 is also treated in detail.

Organisationseinheit(en)

Institut für Theoretische Physik

Typ

Artikel

Journal

Pacific J. Math.

Band

165

Seiten

131-151

Anzahl der Seiten

21

Publikationsdatum

1994

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja