A Remark on Invariants for C*-Algebras of Stable Rank One
Department of Mathematics, University of Toronto, Toronto, M5S 2E4 Canada
Correspondence: Correspondence to be sent to: elliott{at}math.toronto.edu
It is shown that, for a C*-algebra of stable rank one (i.e. in which the invertible elements are dense), two well-known invariants, the Cuntz semigroup and the Thomsen semigroup, contain the same information. More precisely, these two invariants, viewed appropriately, determine each other in a natural way.
References
- Brown L. G., Mingo J. A., Shen N.-T. Quasi-multipliers and embeddings of Hilbert C*-modules. Canadian Journal of Mathematics (1994) 46:1150–74.
- Brown N. P., Perera F., Toms A. S. The Cuntz semigroup, the Elliott conjecture, and dimension functions on C*-algebras. Journal für die reine und angewandte Mathematik. (forthcoming).
- Choi M.-D., Elliott G. A. Density of the set of selfadjoint elements with finite spectrum in an irrational rotation C*-algebra. Mathematica Scandinavica (1990) 67:73–86.[Web of Science]
- Ciuperca A., Robert L., Santiago L. Cuntz semigroup of ideals and quotients and a generalized Kasparov stabilization theorem. Journal of Operator Theory. (forthcoming).
- Coward K. T., Elliott G. A., Ivanescu C. The Cuntz semigroup as an invariant for C*-algebras. Journal für die reine und angewandte Mathematik. (forthcoming).
- Cuntz J. Dimension functions on simple C*-algebras. Mathematische Annalen (1978) 233:145–53.[CrossRef][Web of Science]
- Elliott G. A. On the classification of inductive limits of sequences of semisimple finite-dimensional algebras. Journal of Algebra (1976) 38:29–44.[CrossRef][Web of Science]
- Elliott G. A. Hilbert modules over a C*-algebra of stable rank one. Comptes Rendus Mathématiques de l'Academie des Sciences de la Societé Royale du Canada (2007) 29:48–51.
- Elliott G. A. A classification of certain simple C*-algebras. In: Quantum and Non-Commutative Analysis—Araki H., et al, eds. (1993) Dordrecht, The Netherlands: Kluwer Academic. 373–85.
- Elliott G. A. Normal elements of a simple C*-algebra. In: Algebraic Methods in Operator Theory—Curto R., Jorgensen P. E. T., eds. (1994) Basel, Switzerland: Birkhäuser. 109–23.
- Elliott G. A. Towards a theory of classification. Advances in Mathematics. (forthcoming).
- Elliott G. A., Robert L., Santiago L. On the traces of a C*-algebra. (forthcoming).
- Elliott G. A., Toms A. S. Regularity properties in the classification program for separable amenable C*-algebras. Bulletin of the American Mathematical Society. (forthcoming).
- Frank M. Geometrical aspects of Hilbert C*-modules. Positivity (1999) 3:215–43.[CrossRef][Web of Science]
- Ivanescu C. On the classification of continuous trace C*-algebras with spectrum homeomorphic to the closed internal [0, 1]. In: Advances in Operator Algebras and Mathematical Physics (2005) Bucharest, Romania: Theta. 109–35. Theta Series in Advanced Mathematics 5.
- Jensen K. K., Thomsen K. Elements of KK-theory. Mathematics: Theory and Applications (1991) Basel, Switzerland: Birkhäuser.
- Kasparov G. G. Hilbert C*-modules: theorems of Stinespring and Voiculescu. Journal of Operator Theory (1980) 4:133–50.
- Lance E. C. Hilbert C*-Modules. A Tool Kit for Operator Algebraists (1995) 210. Cambridge, MA: Cambridge University Press. London Mathematical Society Lecture Note Series.
- Rørdam M., Winter W. The Jiang-Su algebra revisited. (forthcoming).
- Stevens K. The classification of certain non-simple approximate interval algebras. In: Operator Algebras and Their Applications,—Fillmore P. A., Mingo J. A., eds. (1998) 20. Providence, RI: American Mathematical Society. 105–48. Fields Institute Communications.
- Thomsen K. Inductive limits of interval algebras: unitary orbits of positive elements. Mathematische Annalen (1992) 293:47–63.[CrossRef][Web of Science]
- Toms A. S. On the classification problem for nuclear C*-algebras. Annals of Mathematics. (forthcoming).
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