Fixed point subalgebras of rational higher-dimensional non-commutative tori
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- by Carla Farsi and Neil Watling PDF
- Proc. Amer. Math. Soc. 125 (1997), 209-217 Request permission
Abstract:
We consider the fixed point subalgebras of higher–dimensional rational non–commutative tori induced by finite order automorphisms derived from a diagonal extension of the canonical $SL(2, \mathbb {Z})$ action on rotation algebras. We give an alternative characterization and determine their $K$–theory.References
- Bruce Blackadar, $K$-theory for operator algebras, Mathematical Sciences Research Institute Publications, vol. 5, Springer-Verlag, New York, 1986. MR 859867, DOI 10.1007/978-1-4613-9572-0
- F. Boca, On the flip fixed point algebra in certain non commutative tori, preprint.
- Ola Bratteli, George A. Elliott, David E. Evans, and Akitaka Kishimoto, Noncommutative spheres. I, Internat. J. Math. 2 (1991), no. 2, 139–166. MR 1094701, DOI 10.1142/S0129167X91000090
- O. Bratteli, G. A. Elliott, D. E. Evans, and A. Kishimoto, Noncommutative spheres. II. Rational rotations, J. Operator Theory 27 (1992), no. 1, 53–85. MR 1241115
- Ola Bratteli and Akitaka Kishimoto, Noncommutative spheres. III. Irrational rotations, Comm. Math. Phys. 147 (1992), no. 3, 605–624. MR 1175495
- Berndt A. Brenken, Representations and automorphisms of the irrational rotation algebra, Pacific J. Math. 111 (1984), no. 2, 257–282. MR 734854
- Berndt Brenken, A classification of some noncommutative tori, Proceedings of the Seventh Great Plains Operator Theory Seminar (Lawrence, KS, 1987), 1990, pp. 389–397. MR 1065837, DOI 10.1216/rmjm/1181073114
- G. A. Elliott, On the $K$-theory of the $C^{\ast }$-algebra generated by a projective representation of a torsion-free discrete abelian group, Operator algebras and group representations, Vol. I (Neptun, 1980) Monogr. Stud. Math., vol. 17, Pitman, Boston, MA, 1984, pp. 157–184. MR 731772
- G.A. Elliott and M. Rørdam, The automorphism group of the irrational rotation $C^{*}$–algebra, preprint.
- Carla Farsi and Neil Watling, Fixed point subalgebras of the rotation algebra, C. R. Math. Rep. Acad. Sci. Canada 13 (1991), no. 2-3, 75–80. MR 1112239
- Carla Farsi and Neil Watling, Quartic algebras, Canad. J. Math. 44 (1992), no. 6, 1167–1191. MR 1192412, DOI 10.4153/CJM-1992-070-4
- Carla Farsi and Neil Watling, Elliptic algebras, J. Funct. Anal. 118 (1993), no. 1, 1–21. MR 1245595, DOI 10.1006/jfan.1993.1136
- Carla Farsi and Neil Watling, Cubic algebras, J. Operator Theory 30 (1993), no. 2, 243–266. MR 1305507
- Carla Farsi and Neil Watling, Symmetrized noncommutative tori, Math. Ann. 296 (1993), no. 4, 739–741. MR 1233495, DOI 10.1007/BF01445133
- Raphael Høegh-Krohn and Tor Skjelbred, Classification of $C^{\ast }$-algebras admitting ergodic actions of the two-dimensional torus, J. Reine Angew. Math. 328 (1981), 1–8. MR 636190, DOI 10.1515/crll.1981.328.1
- A. Kumjian, On the $K$-theory of the symmetrized noncommutative torus, C. R. Math. Rep. Acad. Sci. Canada 12 (1990), no. 2-3, 87–89. MR 1062082
- Yasuo Watatani, Toral automorphisms on irrational rotation algebras, Math. Japon. 26 (1981), no. 4, 479–484. MR 634924
Additional Information
- Carla Farsi
- Affiliation: Carla Farsi, Department of Mathematics, University of Colorado, Campus Box 395, Boulder, Colorado 80309–0395.
- MR Author ID: 311031
- Email: farsi@euclid.colorado.edu
- Neil Watling
- Affiliation: Neil Watling, Department of Mathematics, Widener University, 1 University Place, Chester, Pennsylvania 19013-5792
- Email: watling@kuratowski.math.widener.edu
- Received by editor(s): January 27, 1995
- Received by editor(s) in revised form: July 27, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 209-217
- MSC (1991): Primary 46L80, 46L40
- DOI: https://doi.org/10.1090/S0002-9939-97-03578-8
- MathSciNet review: 1350941