Details
| Original language | English |
|---|---|
| Pages (from-to) | 131-151 |
| Number of pages | 21 |
| Journal | Pacific J. Math. |
| Volume | 165 |
| Issue number | 1 |
| Publication status | Published - 1994 |
Abstract
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In: Pacific J. Math., Vol. 165, No. 1, 1994, p. 131-151.
Research output: Contribution to journal › Article › Research › peer review
}
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 -