Simplicity and the stable rank of some free product C*-algebras
نویسندگان
چکیده
منابع مشابه
Simplicity and the Stable Rank of Some Free Product C∗–algebras
A necessary and sufficient condition for the simplicity of the C∗– algebra reduced free product of finite dimensional abelian algebras is found, and it is proved that the stable rank of every such free product is 1. Related results about other reduced free products of C∗–algebras are proved. Introduction The reduced free product of C∗–algebras with respect to given states was introduced indepen...
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It is proved that the reduced group C∗-algebra C∗ red(G) has stable rank one (i.e. its group of invertible elements is a dense subset) if G is a discrete group arising as a free product G1 ∗G2 where |G1| ≥ 2 and |G2| ≥ 3. This follows from a more general result where it is proved that if (A, τ) is the reduced free product of a family (Ai, τi), i ∈ I, of unital C∗-algebras Ai with normalized fai...
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For a row finite directed graph E, Kumjian, Pask, and Rae-burn proved that there exists a universal C *-algebra C * (E) generated by a Cuntz-Krieger E-family. In this paper we consider two density problems of invertible elements in graph C *-algebras C * (E), and it is proved that C * (E) has stable rank one, that is, the set of all invertible elements is dense in C * (E) (or in its unitization...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1999
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-99-02180-7