Limits of certain subhomogeneous $C^*$-algebras
摘要
It is shown that the Elliott invariant is a complete invariant for the simple unital (7*-algebras which can be realized as an inductive limit of a sequence of finite direct sums of algebras of the form {/ e C7(T) 0 Mn : f(x,) C M^ i = 1,2,..., N}, where x\^x^^... ^XN is an arbitrary (finite) set on the circle T and d is a natural number dividing n.The corresponding range of invariants is identified and the classification result is extended to the non-unital case.A series of results about the structure of these (7*-algebras and the maps between them are also obtained.Resume.-On prouve que Pinvariant d'Elliott est un invariant complet des (7*-algebres simples a element unite qui peuvent etre realisees comme limite inductive d'une suite de sommes finies d'algebres de la forme {/ C G(T) Mn : f(xi) Md, i = 1,2,... , TV} , ou {x\^ x^^'' , xpf} C T est un sous-ensemble arbitraire et d un entier divisant n.On determine Pensemble des valeurs prises par Pinvariant et on etend la classification aux algebres sans unite.Par ailleurs on donne une serie de resultats sur la structure de ces (7*-algebres.