TY - JOUR

T1 - q-canonical commutation relations and stability of the Cuntz algebra

AU - Jo rgensen, P. E. T.

AU - Schmitt, L. M.

AU - Werner, R. F.

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

M3 - Article

VL - 165

SP - 131

EP - 151

JO - Pacific J. Math.

JF - Pacific J. Math.

IS - 1

ER -