Finite sums and products of commutators in inductive limit $C^{*}$-algebras

Thomsen, Klaus

Annales de l'Institut Fourier, Volume 43 (1993) no. 1, pp. 225-249.

Results of T. Fack, P. de la Harpe and G. Skandalis concerning the internal structure of simple $AF$-algebras are extended to $C^{*}$-algebras that are inductive limits of finite direct sums of homogeneous $C^{*}$-algebras. The generalizations are obtained with slightly varying assumptions on the building blocks, but all results are applicable to unital simple inductive limits of finite direct sums of circle algebras.

Des résultats de T. Fack, P. de La Harpe et G. Skandalis sur la structure interne des $AF$-algèbres simples sont généralisés à des $C^{*}$-algèbres qui sont limites inductives de sommes directes finies de $C^{*}$-algèbres homogènes. Les généralisations sont obtenues sous diverses hypothèses concernant les $C^{*}$-algèbres dont les constructions dépendent; mais tous les résultats sont valables pour les limites inductives (avec unité) de sommes directes finies d’algèbres de matrices à coefficients dans les fonctions continues sur le cercle.

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