A simple, monotracial, stably projectionless C *‐algebra
نویسندگان
چکیده
منابع مشابه
A simple, monotracial, stably projectionless C*-algebra
We construct a simple, nuclear, stably projectionless C∗-algebra W which has trivial Ktheory and a unique tracial state, and we investigate the extent to which W might fit into the hierarchy of strongly self-absorbing C∗-algebras as an analogue of the Cuntz algebra O2. In this context, we show that every nondegenerate endomorphism of W is approximately inner and we construct a tracepreserving e...
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This paper explores the following regularity properties and their relationships for simple, not-necessarily-unital C∗algebras: (i) Jiang-Su stability, (ii) unperforation in the Cuntz semigroup, and (iii) slow dimension growth (applying only in the case that the C∗-algebra is approximately subhomogeneous). An example is given of a simple, separable, nuclear, stably projectionless C∗-algebra whos...
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Let G be an inductive limit of finite cyclic groups and let A be a unital simple projectionless C∗-algebra with K1(A) = G and with a unique tracial state, as constructed based on dimension drop algebras by Jiang and Su. First, we show that any two aperiodic elements in Aut(A)/WInn(A) are conjugate, where WInn(A) means the subgroup of Aut(A) consisting of automorphisms which are inner in the tra...
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We construct a unital pre-C*-algebra A0 which is stably finite, in the sense that every left invertible square matrix over A0 is right invertible, while the C*-completion of A0 contains a non-unitary isometry, and so it is infinite. To appear in Proceedings of the American Mathematical Society.
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The main result here is that a separable C∗-algebra is Z-stable (where Z denotes the Jiang-Su algebra) if (i) it has finite nuclear dimension or (ii) it is approximately subhomogeneous with slow dimension growth. This generalizes the main results of [27, 36] to the nonunital setting. Algebraic simplicity is established as a fruitful weakening of being simple and unital, and the proof of the mai...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2012
ISSN: 0024-6107,1469-7750
DOI: 10.1112/jlms/jds049