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Some C*-Algebras with Outer Derivations, II

  • George A. Elliott (a1)

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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.

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References

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1. Bratteli, O., Inductive limits of finite dimensional C*'-algebras, Trans. Amer. Math. Soc. 171 (1972), 195234.
2. Dauns, J. and Hofmann, K. H., Representations of rings by sections, Mem. Amer. Math. Soc. 83 (1968).
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Some C*-Algebras with Outer Derivations, II

  • George A. Elliott (a1)

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