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An action of the Klein four-group on the irrational rotation C*-algebra

Published online by Cambridge University Press:  17 April 2009

P.J. Stacey
P.J. Stacey
Affiliation:
School of MathematicsLa Trobe UniversityBundoora Vic 3083Australia e-mail: [email protected]
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Abstract

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Explicit automorphisms of the irrational rotation algebra are constructed which are associated with the two 2 × 2 diagonal integer matrices of determinant −1. The fixed point algebra of the product of these two automorphisms is shown to be isomorphic to the fixed point algebra of the flip.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 1 , August 1997 , pp. 135 - 148
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Blackadar, B., K-theory for operator algebras (Springer-Verlag, Berlin, Heidelberg, New York, 1986).CrossRefGoogle Scholar
[2]Blackadar, B., ‘Traces on simple AF C*-algebras’, J. Funct. Anal. 38 (1980), 156–168.CrossRefGoogle Scholar
[3]Bratteli, O., Elliott, G.A., Evans, D.E. and Kishimoto, A., ‘Non-commutative spheres I’, Internat. J. Math. 2 (1991), 139–166.CrossRefGoogle Scholar
[4]Bratteli, O., Elliott, G.A., Evans, D.E. and Kishimoto, A., ‘Non-commutative spheres II: rational rotations’, J. Operator Theory 27 (1992), 53–85.Google Scholar
[5]Bratteli, O. and Kishimoto, A., ‘Non-commutative spheres III: irrational rotations’, Comm. Math. Phys. 147 (1992), 605–624.CrossRefGoogle Scholar
[6]Brenken, B., ‘Representations and automorphisms of the irrational rotation algebra’, Pacific J. Math. 111 (1984), 257–282.CrossRefGoogle Scholar
[7]Dixmier, J., Les C*-algèbres et leurs représentations (Gauthier-Villars, Paris, 1964).Google Scholar
[8]Elliott, G.A., ‘On the classification of C*-algebras of real rank zero’, J. Reine Angew. Math. 443 (1993), 179–219.Google Scholar
[9]Elliott, G.A. and Evans, D.E., ‘The structure of the irrational rotation C*-algebra’, Ann. of Math. 138 (1993), 477–501.CrossRefGoogle Scholar
[10]Evans, D.E. and Kishimoto, A., ‘Compact group actions on UHF algebras obtained by folding the interval’, J. Funct. Anal. 98 (1991), 346–360.CrossRefGoogle Scholar
[11]Kumjian, A., ‘On the K-theory of the symmetrized non-commutative torus’, C.R. Math. Rep. Acad. Sci. Canada 12 (1990), 87–89.Google Scholar
[12]Pedersen, G.K., C*-algebras and their automorphism groups (Academic Press, London, 1979).Google Scholar
[13]Su, H., ‘On the classification of C*-algebras of real rank zero: inductive limits of matrix algebras over graphs’, C.R. Math. Rep. Acad. Sci. Canada 13 (1991), 223–228.Google Scholar
[14]Su, H., ‘On the classification of C*-algebras of real rank zero: inductive limits of matrix algebras over non-Hausdorff graphs’, Mem. Amer. Math. Soc. 547 (1995).Google Scholar
[15]Walters, S.G., ‘Projective modules over the non-commutative sphere’, J. London Math. Soc. 51 (1995), 589–602.CrossRefGoogle Scholar
[16]Walters, S.G., ‘Inductive limit automorphisms of the irrational rotation algebra’, Comm. Math. Phys. 171 (1995), 365–381.CrossRefGoogle Scholar
[17]Watatani, Y., ‘Toral automorphisms on irrational rotation algebras’, Math. Japon 26 (1981), 479–484.Google Scholar