CertainC*-algebras with real rank zero and their corona and multiplier algebras: II

Zhang, Shuang

doi:10.1007/bf00961332

Cited by 11 publications

(3 citation statements)

References 27 publications

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“…Note that both q i (t i ) and q i+1 (t i ) are nontrivial. Therefore Theorem 1.1 of [Zh2] implies that these two projections are homotopic. Using the previous lemma, we now construct q on [0, t 1 ] so that q(0) = e 0 and q(t 1 ) = q 1 (t 1 ), on [t 1 , t 2 ] so that q(t 1 ) = q 1 (t 1 ) and q(t 2 ) = q 2 (t 2 ), etc., finishing by constructing q on [t n−1 , 1 2 (t n−1 + 1)] so that q(t n−1 ) = q n−1 (t n−1 ) and q( 1 2 (t n−1 + 1)) = q n ( 1 2 (t n−1 + 1)) and on [ 1 2 (t n−1 + 1), 1] so that q( 1 2 (t n−1 + 1)) = q n ( 1 2 (t n−1 + 1)) and q(1) = e 1 .…”

Section: Notationmentioning

confidence: 89%

Classification of direct limits of even Cuntz-circle algebras

Lin¹,

Phillips²

1996

Memoirs of the AMS

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We prove a classification theorem for purely infinite simple C * -algebras that is strong enough to show that the tensor products of two different irrational rotation algebras with the same even Cuntz algebra are isomorphic. In more detail, let C be the class of simple C * -algebras A which are direct limits A ∼ = limwhere m is even, O m is the Cuntz algebra, and X is either a point, a compact interval, or the circle S 1 , and each map A k → A is approximately absorbing. ("Approximately absorbing" is defined in Section 1.) We show that two unital C * -algebras A and B in C are isomorphic if and only ifThis class is large enough to exhaust all possible K-groups: if G 0 and G 1 are countable odd torsion (abelian) groups and g ∈ G 0 , then there is a). The class C contains the tensor products of irrational rotation algebras with even Cuntz algebras. It is also closed under the formation of hereditary subalgebras, countable direct limits (provided that the direct limit is simple), and tensor products with simple AF algebras.

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Section: Notationmentioning

confidence: 89%

Classification of direct limits of even Cuntz-circle algebras

Lin¹,

Phillips²

1996

Memoirs of the AMS

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“…It is well-known that every σ -unital purely infinite simple C * -algebra is either unital or stable [23]. Theorem 2.1.…”

Section: Resultsmentioning

confidence: 96%

“…However, for certain C * -algebras, p ∼ q if and only if p ∼ h q provided that p and q are projections of neither 0 nor 1. AF algebras and purely infinite simple C * -algebras are examples of such C * -algebras [20]. For the case of extension algebras, we have the following results.…”

Section: Proofmentioning

confidence: 97%