The generator problem for $\mathcal {Z}$-stable $C^*$-algebras
نویسندگان
چکیده
منابع مشابه
Homomorphisms into Simple Z-stable C∗-algebras
Let A and B be unital separable simple amenable C*-algebras which satisfy the Universal Coefficient Theorem. Suppose that A and B are Z-stable and are of rationally tracial rank no more than one. We prove the following: Suppose that φ, ψ : A → B are unital *monomorphisms. There exists a sequence of unitaries {un} ⊂ B such that lim n→∞ unφ(a)un = ψ(a) for all a ∈ A, if and only if [φ] = [ψ] in K...
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Let Z denote the simple limit of prime dimension drop algebras that has a unique tracial state (cf. Jiang and Su [11]). Let A 6= 0 be a unital C∗-algebra with A ∼= A ⊗ Z. Then the homotopy groups of the group U(A) of unitaries in A are stable invariants, namely, πi(U(A)) ∼= Ki−1(A) for all integer i ≥ 0. Furthermore, A has cancellation for full projections, and satisfies the comparability quest...
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The Jiang–Su algebra Z has come to prominence in the classification program for nuclear C-algebras of late, due primarily to the fact that Elliott’s classification conjecture predicts that all simple, separable, and nuclear C-algebras with unperforated K-theory will absorb Z tensorially (i.e., will be Z-stable). There exist counterexamples which suggest that the conjecture will only hold for si...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2014
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2014-06013-3