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

Thomsen, Klaus

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

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.

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.

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