Extensions by Simple C*-Algebras: Quasidiagonal Extensions
نویسندگان
چکیده
منابع مشابه
Extensions of Quasidiagonal C * -algebras and K-theory
Let 0 → I → E → B → 0 be a short exact sequence of C*-algebras whereE is separable, I is quasidiagonal (QD) andB is nuclear, QD and satisfies the UCT. It is shown that if the boundary map ∂ : K1(B) → K0(I) vanishes then E must be QD also. A Hahn-Banach type property for K0 of QD C ∗-algebras is also formulated. It is shown that every nuclear QD C∗-algebra has this K0Hahn-Banach property if and ...
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to be quasidiagonal when B⊗K contains an approximate unit of projections which is quasi-central in E, cf. [Sa]. He identified, under certain conditions, the subgroup of KK(A,B) which the quasidiagonal extensions correspond to under Kasparov’s isomorphism Ext(A,B) ' KK(A,B). C. Schochet has removed some of Salinas’ conditions in [S], the result being that when A is a unital C-algebra in the boot...
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We give a detailed survey of the theory of quasidiagonal C∗-algebras. The main structural results are presented and various functorial questions around quasidiagonality are discussed. In particular we look at what is currently known (and not known) about tensor products, quotients, extensions, free products, etc. of quasidiagonal C∗-algebras. We also point out how quasidiagonality is connected ...
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Using extension theory and recent results of Elliott and Gong we exhibit new classes of nuclear stably finite C∗-algebras , which have real rank zero and stable rank one, and are classified by K-theoretical data. Various concepts of quasidiagonality are employed to show that these C*-algebras are not inductive limits of (sub)homogeneous C∗-algebras.
متن کامل(apd)–property of C∗–algebras by Extensions of C∗–algebras with (apd)
A unital C∗–algebra A is said to have the (APD)–property if every nonzero element in A has the approximate polar decomposition. Let J be a closed ideal of A. Suppose that J̃ and A/J have (APD). In this paper, we give a necessary and sufficient condition that makes A have (APD). Furthermore, we show that if RR(J ) = 0 and tsr(A/J ) = 1 or A/J is a simple purely infinite C∗–algebra, then A has (APD).
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2005
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2005-016-5