Abstract
In this paper, we show that, without involving theC*-bundle theory, elementary differential topology can do the classification of homogeneousC*-crossed productC(X) xα Z, whereX is a compact differentiable manifold of low dimension and α is a diffeomorphism ofX. The motivation of this work is the Shultz's theorem which states that aC*-algebra can be identified with its pure state space carryingw*-topology and certain geometric structure.
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References
Shultz, F. W.,Pure states as a dual object for C*-algebras, Commun. Math. Phys.,82 (1982), 497–509.
Hoegh-Krohn, R. and Skjebred, T.,Classification of C*-algebras admiting ergodic actions of two-dimensional torus, J. Reine Angew. Math.,328(1981), 1–8.
Li, B. and Lin, Q.,Pure state space of C(X) xα Z with αn = id., Lecture Notes in Contemporary Math., Inst. of Math., Acad. Sinica,2(1991), 147–162.
Bott, R. and Tu., L. W., Differential Forms in Algebraic Topology, Springer-Verlag, New York/Berlin, 1982.
Li, B. and Lin, Q.,Pure state approach to C(X) xα Z n , Chin. Ann. of Math.,16B:1 1995, 1–12.
Steenrod, N., The Topoloyg of Fibre Bundles, Princeton University Press, Princeton, NJ, 1951.
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Lin, Q. Differential structure of certainC(X) xα Z . Acta Mathematica Sinica 11, 225–231 (1995). https://doi.org/10.1007/BF02265387
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DOI: https://doi.org/10.1007/BF02265387