Hostname: page-component-84b7d79bbc-fnpn6 Total loading time: 0 Render date: 2024-08-02T09:12:14.060Z Has data issue: false hasContentIssue false
  • English
  • Français

Some C*-Algebras with Outer Derivations, II

Published online by Cambridge University Press:  20 November 2018

George A. Elliott
George A. Elliott*
Affiliation:
The Institute for Advanced Study, Princeton, New Jersey
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.

In this paper we shall consider the class of C*-algebras which are inductive limits of sequences of finite-dimensional C*-algebras. We shall give a complete description of those C*-algebras in this class every derivation of which is inner.

Theorem. Let A be a C*-algebra. Suppose that A is the inductive limit of a sequence of finite-dimensional C*-algebras. Then the following statements are equivalent:

(i) every derivation of A is inner;

(ii) A is the direct sum of a finite number of algebras each of which is either commutative, the tensor product of a finite-dimensional and a commutative with unit, or simple with unit.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 185 - 189
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Bratteli, O., Inductive limits of finite dimensional C*'-algebras, Trans. Amer. Math. Soc. 171 (1972), 195–234.Google Scholar
2. Dauns, J. and Hofmann, K. H., Representations of rings by sections, Mem. Amer. Math. Soc. 83 (1968).Google Scholar
3. Elliott, G. A., Derivations of matroid C*-algebras, Invent. Math. 9 (1970), 253–269.Google Scholar
4. Elliott, G. A., Some C*-algebras with outer derivations, Rocky Mountain J. Math. 3 (1973), 501–506.Google Scholar
5. Fell, J. M. G., The structure of algebras of operator fields, Acta Math. 106 (1961), 233–280.Google Scholar
6. Kaplansky, I., The structure of certain operator algebras, Trans. Amer. Math. Soc. 70 (1951), 219–255.Google Scholar
7. Kaplansky, I., Group algebras in the large, Tôhoku Math. J. 3 (1951), 249–256.Google Scholar
8. Sakai, S., Derivations of simple C*-algebras, J. Functional Analysis 2 (1968), 202–206.Google Scholar
9. Sakai, S., Derivations of simple C*-algebras, III, Tôhoku Math. J. 23 (1971), 559–564.Google Scholar
10. Sakai, S., Derived C*-algebras of primitive C*-algebras (to appear).Google Scholar
11. Singer, I. M. and Wermer, J., Derivations on commutative normed algebras, Math. Ann. 129 (1955), 260–264.Google Scholar