# FINITE-DIMENSIONAL REPRESENTATIONS OF FREE PRODUCT C*-ALGEBRAS

@article{Exel1992FINITEDIMENSIONALRO, title={FINITE-DIMENSIONAL REPRESENTATIONS OF FREE PRODUCT C*-ALGEBRAS}, author={Ruy Exel and Terry A. Loring}, journal={International Journal of Mathematics}, year={1992}, volume={03}, pages={469-476} }

Our main theorem is a characterization of C*-algebras that have a separating family of finite-dimensional representations. This characterization makes possible a solution to a problem posed by Goodearl and Menaul. Specifically, we prove that the free product of such C*-algebras again has this property.

## 81 Citations

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### PRIMITIVITY OF UNITAL FULL FREE PRODUCTS OF FINITE DIMENSIONAL C ∗ -ALGEBRAS

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A C � -algebra is called primitive if it admits a faithful and irreducible ∗-representation. We show that the unital C � - algebra full free product, A = A1 ∗ A2, of nontrivial finite dimen- sional C…

### Operator Spaces and Residually Finite-Dimensional C*-Algebras

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The noncommutative analog of an approximative absolute retract (AAR) is introduced, a weakly projective C*-algebra. This property sits between being residually finite dimensional and projectivity.…

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We prove that an amalgamated free product of separable commutative C*-algebras is residually finite-dimensional.

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The soft tori constitute a continuous deformation, in a very precise sense, from the commutative C -algebra C(T 2 ) to the highly non-commutative C -algebra C (F2). Since both of these C -algebras…

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For every operator space $X$ the $C^\ast$-algebra containing it in a universal way is residually finite-dimensional (that is, has a separating family of finite-dimensional representations). In…

## 4 References

### THE FULL C* -ALGEBRA OF THE FREE GROUP ON TWO GENERATORS

- Mathematics
- 1980

1* Introduction. We present a "generic" C*-algebra in illustration of several peculiar phenomena that may occur in the theory of representations. Let F2 denote the free group on two generators. If π…

### Weak Containment and Induced Representations of Groups

- MathematicsCanadian Journal of Mathematics
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Let G be a locally compact group and G† its dual space, that is, the set of all unitary equivalence classes of irreducible unitary representations of G. An important tool for investigating the group…