Definiamo relazioni canoniche discretizzate associate ad automorfismi di ordine finito di gruppi abeliani discreti. Questa è una generalizzazione di autoe Á morfismi di ordine finito di algebre di rotazione. Si dimostrano anche proprieta di particolari operatori di Schrödinger che derivano da queste relazioni.
Referenze Bibliografiche
[1] W. ARVESON, Discretized CCR algebras, J. Operator Theory, 26 (1991), 225-239.
[2]
W. ARVESON,
Non-commutative spheres and numerical quantum mechanics,
Operator algebras, mathematical physics and low dimensional topology, 1-10. |
Zbl 0803.46078[3]
O. BRATTELI -
G.A. ELLIOTT -
D.E. EVANS -
A. KISHIMOTO,
Non commutative spheres I,
International. J. Math.,
2 (
1991), 139-166. |
Zbl 0759.46063[4]
O. BRATTELI -
G.A. ELLIOTT -
D.E. EVANS -
A. KISHIMOTO,
Non commutative spheres II, Rational Rotations,
J. Operator Theory,
27 (
1992), 53-85. |
Zbl 0814.46060[5]
O. BRATTELI -
A. KISHIMOTO,
Non commutative spheres III, Irrational Rotations,
Commun. Math. Phys.,
147 (
1992), 605-624. |
Zbl 0772.46040[6] M.-
D. CHOI -
G. ELLIOTT -
N. YUI,
Gauss polynomials and the rotation algebra,
Inv. Math.,
99 (
1990), 225-246. |
fulltext EuDML |
Zbl 0665.46051[7] G.A. ELLIOTT, On the K-theory of the $C^*$-algebra generated by a projective representation of a torsion-free discrete abelian group, Operator Algebras and Group Representations, 1 Pitman, London (1984), 157-184.
[8] G.A. ELLIOTT, Gaps in the spectrum of an almost Schrödinger operator, Geometric Methods in Operator Algebras-Proceedings of the US-Japan Conference July 11-15 (1983), 181-191.
[9] C. FARSI - N. WATLING, Quartic algebras, Can. J. Math, 44 (1992), 1167-1191.
[10]
C. FARSI -
N. WATLING,
Fixed point subalgebras of the rotation algebra,
C.R. Math. Rep. Acad. Sci. Canada,
XIII (
1991), 75-80. |
Zbl 0743.46071[11]
C. FARSI -
N. WATLING,
Trivial fixed point subalgebras of the rotation algebra,
Math. Scand.,
72 (
1993), 298-302. |
fulltext EuDML |
Zbl 0795.46051[12] C. FARSI - N. WATLING, Cubic algebras, J. Operator Theory, 30 (1993), 243-266.
[13] C. FARSI - N. WATLING, Elliptic algebras, J. Functional Analysis, 118 (1993), 1-21.
[14]
C. FARSI -
N. WATLING,
Abstract characterization of the fixed point subalgebras of the rotation algebra,
Canad. J. Math.,
46 (
1994), 1211-1237. |
Zbl 0811.46068[15]
C. FARSI -
N. WATLING,
Symmetrized non-commutative tori,
Math. Ann.,
296 (
1993), 739-741. |
fulltext EuDML[16]
C. FARSI -
N. WATLING,
Fixed Point Subalgebras of Rational Higher Dimensional Non-Commutative Tori,
Proc. Amer. Math. Soc.,
125 (
1997), 209-217. |
Zbl 0860.46046[17] N. RIEDEL, Almost Mathieu operators and rotation $C^*$-algebras, Proc. London Math. Soc., 56 (1988), 281-302.
[18]
N. RIEDEL,
On spectral properties of almost Mathieu operators and connections with irrational rotation algebras,
Rocky Mount. Jour. Math.,
20 (
1990), 539-548. |
Zbl 0745.46064[19]
N. RIEDEL,
Absence of Cantor spectrum for a class of Schrödinger operators,
Bull. AMS,
29 (
1993), 85-87. |
Zbl 0796.47029[20]
M.A. RIEFFEL,
$C^*$-algebras associated with irrational rotations,
Pacific J. Math.,
93 (
1981), 415-429. |
Zbl 0499.46039[21]
M.A. RIEFFEL,
Projective modules over higher dimensional non-commutative tori,
Can. J. Math.,
40 (
1988), 257-338. |
Zbl 0663.46073[22]
M.A. RIEFFEL,
Non-commutative tori – A case study of non-commutative differentiable manifolds,
Contemporary Mathematics,
105 (
1990), 191-211. |
Zbl 0713.46046
Con il contributo del Ministero per i Beni e le Attività Culturali