Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T13:37:37.918Z Has data issue: false hasContentIssue false
  • English
  • Français

Nuclear subalgebras of UHF C*-algebras

Published online by Cambridge University Press:  20 January 2009

R. J. Archbold  and
Alexander Kumjian
R. J. Archbold
Affiliation:
Department of Mathematics, University of California, Santa Barbara, California, 93106, USA
Alexander Kumjian
Affiliation:
School of Mathematics, University of New South Wales, Kensington, N.S.W. 2033, Australia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A C*-algebra A is said to be approximately finite dimensional (AF) if it is the inductive limit of a sequence of finite dimensional C*-algebras(see [2], [5]). It is said to be nuclear if, for each C*-algebra B, there is a unique C*-norm on the *-algebraic tensor product A ⊗B [11]. Since finite dimensional C*-algebras are nuclear, and inductive limits of nuclear C*-algebras are nuclear [16];,every AF C*-algebra is nuclear. The family of nuclear C*-algebras is a large and well-behaved class (see [12]). The AF C*-algebras for a particularly tractable sub-class which has been completely classified in terms of the invariant K0 [7], [5].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 1 , February 1986 , pp. 97 - 100
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

REFERENCES

1.Blackadar, B., Nonnuclear subalgebras of C*-algebras, J. Operator Theory, (to appear).Google Scholar
2.Bratteli, O., Inductive limits of finite dimensional C*-algebras, Trans. Amer. Math. Soc. 171 (1972), 195–234.Google Scholar
3.Brown, L., Stable isomorphism of hereditary subalgebras of C*-algebras, Pacific J. Math. 71 (1977), 335–348.CrossRefGoogle Scholar
4.Choi, M–D., A simple C*-algebra generated by two finite-order unitaries, Canad. J. Math. 31 (1979), 867–880.Google Scholar
5.Effros, E. G., Dimensions and C*-algebras (CBMS Regional Conference Series No. 46, Amer. Math. Soc, Providence, R.I., 1981).CrossRefGoogle Scholar
6.Effros, E. G., On the structure of C*-algebras: Some old and new problems, Proc. Symp. Pure Math. 38 (1982), 19–34.CrossRefGoogle Scholar
7.Elliott, G. A., On the classification of inductive limits of sequences of semi-simple finite dimensional algebras, J. Algebra 38 (1976), 29–44.CrossRefGoogle Scholar
8.Elliott, G. A., Automorphisms determined by multipliers on ideals of a C*-algebra, J. Functional Analysis 23 (1976), 1–10.CrossRefGoogle Scholar
9.Glimm, J., On a certain class of operator algebras, Trans. Amer. Math. Soc. 95 (1960), 318–340.CrossRefGoogle Scholar
10.Kumjian, A., On C*-diagonals, preprint.Google Scholar
11.Lance, E. C., On nuclear C*-algebras, J. Functional Analysis 12 (1973), 157–176.CrossRefGoogle Scholar
12.Lance, E. C., Tensor products and nuclear C*-algebras, Proc. Symp. Pure Math. 38 (1982), 379–399.CrossRefGoogle Scholar
13.Pedersen, G. K., C*-algebras and their automorphism groups (Academic Press, London, 1979).Google Scholar
14.Powers, R. T., Representations of uniformly hyperfinite algebras and their associated Von Neumann rings, Annals of Math. 86 (1967), 138–171.CrossRefGoogle Scholar
15.Stratila, S. and Voiculescu, D., Representations of AF algebras and of the group U(∞) (Lecture notes in Math. 486, Springer-Verlag, Berlin, 1975).Google Scholar
16.Takesaki, M., On the cross-norm of the direct product of C*-algebras, Tôhoku Math. J. 16 (1964), 111–122.CrossRefGoogle Scholar
17.Wassermann, A. S., The slice map problem for C*-algebras, Proc. London Math. Soc. (3) 32 (1976), 537–559.CrossRefGoogle Scholar