Geodesic
Discretized C∗-Algebras
Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 3, pp. 697-709.

Voir la notice de l'article dans Biblioteca Digitale Italiana di Matematica

We define discretized canonical commutation relations associated to finite order automorphisms of discrete abelian groups. This generalizes the situation for rotation algebras and their finite order automorphisms. We also consider the almost Schrödinger operator associated to the given commutation relations.
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. 
@article{BUMI_2006_8_9B_3_a11,
     author = {Farsi, Carla and Watling, Neil},
     title = {Discretized $C^*${-Algebras}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {697--709},
     publisher = {mathdoc},
     volume = {Ser. 8, 9B},
     number = {3},
     year = {2006},
     zbl = {1178.46051},
     mrnumber = {2274121},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_3_a11/}
}
TY  - JOUR
AU  - Farsi, Carla
AU  - Watling, Neil
TI  - Discretized $C^*$-Algebras
JO  - Bollettino della Unione matematica italiana
PY  - 2006
SP  - 697
EP  - 709
VL  - 9B
IS  - 3
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_3_a11/
LA  - en
ID  - BUMI_2006_8_9B_3_a11
ER  - 
%0 Journal Article
%A Farsi, Carla
%A Watling, Neil
%T Discretized $C^*$-Algebras
%J Bollettino della Unione matematica italiana
%D 2006
%P 697-709
%V 9B
%N 3
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_3_a11/
%G en
%F BUMI_2006_8_9B_3_a11
Farsi, Carla; Watling, Neil. Discretized $C^*$-Algebras. Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 3, pp. 697-709. https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_3_a11/

[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

[3] O. Bratteli - G.A. Elliott - D.E. Evans - A. Kishimoto, Non commutative spheres I, International. J. Math., 2 (1991), 139-166. | Zbl

[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

[5] O. Bratteli - A. Kishimoto, Non commutative spheres III, Irrational Rotations, Commun. Math. Phys., 147 (1992), 605-624. | Zbl

[6] M.-D. Choi - G. Elliott - N. Yui, Gauss polynomials and the rotation algebra, Inv. Math., 99 (1990), 225-246. | fulltext EuDML | Zbl

[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

[11] C. Farsi - N. Watling, Trivial fixed point subalgebras of the rotation algebra, Math. Scand., 72 (1993), 298-302. | fulltext EuDML | Zbl

[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

[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

[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

[19] N. Riedel, Absence of Cantor spectrum for a class of Schrödinger operators, Bull. AMS, 29 (1993), 85-87. | Zbl

[20] M.A. Rieffel, $C^*$-algebras associated with irrational rotations, Pacific J. Math., 93 (1981), 415-429. | Zbl

[21] M.A. Rieffel, Projective modules over higher dimensional non-commutative tori, Can. J. Math., 40 (1988), 257-338. | Zbl

[22] M.A. Rieffel, Non-commutative tori – A case study of non-commutative differentiable manifolds, Contemporary Mathematics, 105 (1990), 191-211. | Zbl