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The positive cones of k0-groups of crossed products associated with Furstenberg transformations on the 2-torus

Published online by Cambridge University Press:  20 January 2009

Kazunori Kodaka
Kazunori Kodaka
Affiliation:
Department of Mathematical Sciences, College of Science, Ryukyu University, Nishihara-cho, Okinawa, 908-0213, Japan
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Abstract

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Let θ be an irrational number in (0,1) and f a real-valued continuous function on the 1-torus T. Letφθ, f be a Furstenberg transformation on the 2-torus T2 defined by for any (t, s) ∈ T2, where ρ is a non-zero integer, and we identify a function on T or T2 with a function on R or R2 with period 1, respectively. Let Aθ, f be the crossed product associated with φθ, f. In this paper we wiil compute the positive cone of the K0-group of Aθ, f.

Keywords

crossed productequivalence bimodulefull projectionFurstenberg transformationK0-grouppositive cone
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 1 , February 2000 , pp. 167 - 175
Copyright
Copyright © Edinburgh Mathematical Society 2000

References

1.Brown, L. G., Stable isomorphism of hereditary subalgebras of C*-algebras, Pacific J. Math. 71 (1977), 335–348.Google Scholar
2.Combes, F., Crossed products and Morita equivalence, Proc. Lond. Math. Soc. 49 (1984), 289–306.Google Scholar
3.Connes, A., An analogue of the Thom isomorphism for crossed products of a C*-algebra by an action of R, Adv. Math. 39 (1981), 31–55.Google Scholar
4.Ji, R., On the crossed product C*-algebras associated with Furstenberg transformations on tori. Ph.D. thesis, State University of New York at Stony Brook (1986).Google Scholar
5.Kodaka, K., K-theory for the C*-algebra of the discrete Heisenberg group, Tokyo J. Math. 9 (1986), 365–372.Google Scholar
6.Kodaka, K., Automorphisms of tensor products of irrational rotation C*-algebras and the C*-algebra of compact operators. II, J. Operator Theory 30 (1993), 77–84.Google Scholar
7.Kodaka, K., Anzai and Furstenberg transformations on the 2-torus and topologically quasi-discrete spectrum, Can. Math. Bull. 38 (1995), 87–92.Google Scholar
8.Kodaka, K., Picard groups of irrational rotation C*-algebras, J. Lond. Math. Soc. 56 (1997), 179–188.Google Scholar
9.Kodaka, K., Full projections, equivalence bimodules and automorphisms of stable algebras of unital C*-algebras, J. Operator Theory 37 (1997), 357–369.Google Scholar
10.Packer, J., C*-algebras generated by projective representations of the discrete Heisenberg group, J. Operator Theory 18 (1987), 41–66.Google Scholar
11.Packer, J., Strong Morita equivalence for Heisenberg C*-algebras and the positive cones of their K 0-groups, Can. J. Math. 40 (1988), 833–864.Google Scholar
12.Pedersen, G. K., C*-algebras and their automorphisms groups (Academic, London, 1979).Google Scholar
13.Pimsner, M. and Voiculescu, D., Exact sequences for K-groups and Ext-groups of certain cross-product C*-algebras, J. Operator Theory 4 (1980), 93–118.Google Scholar
14.Rieffel, M. A., Induced representations of C*-algebras, Adv. Math. 13 (1974), 176–257.Google Scholar
15.Rieffel, M. A., C*-algebras associated with irrational rotations, Pacific J. Math. 93 (1981), 415–429.CrossRefGoogle Scholar
16.Rieffel, M. A., The cancellation theorem for projective modules over irrational rotation C*-algebras, Proc. Lond. Math. Soc. 47 (1983), 285–302.Google Scholar
17.Rouhani, H., A Furstenberg transformation of the 2-torus without quasi-discrete spectrum, Can. Math. Bull. 33 (1990), 316–322.CrossRefGoogle Scholar