The Cuntz-Pimsner extension and mapping cone exact sequences
نویسندگان
چکیده
منابع مشابه
On Certain Cuntz-pimsner Algebras
Let A be a separable unital C*-algebra and let π : A → L(H) be a faithful representation of A on a separable Hilbert space H such that π(A) ∩ K(H) = {0}. We show that OE , the Cuntz-Pimsner algebra associated to the Hilbert A-bimodule E = H⊗C A, is simple and purely infinite. If A is nuclear and belongs to the bootstrap class to which the UCT applies, then the same applies to OE . Hence by the ...
متن کاملExactness of Cuntz–pimsner C–algebras
Let H be a full Hilbert bimodule over a C-algebra A. We show that the Cuntz–Pimsner algebra associated to H is exact if and only if A is exact. Using this result, we give alternative proofs for exactness of reduced amalgemated free products of exact C– algebras. In the case that A is a finite–dimensional C–algebra, we also show that the Brown–Voiculescu topological entropy of Bogljubov automorp...
متن کاملCuntz-Pimsner C-algebras associated with subshifts
By using C∗-correspondences and Cuntz-Pimsner algebras, we associate to every subshift (also called a shift space) X a C∗-algebra OX, which is a generalization of the Cuntz-Krieger algebras. We show that OX is the universal C ∗-algebra generated by partial isometries satisfying relations given by X. We also show thatOX is a one-sided conjugacy invariant of X.
متن کاملOn the nuclearity of certain Cuntz-Pimsner algebras
In the present paper, we give a short proof of the nuclearity property of a class of CuntzPimsner algebras associated with a HilbertA-bimodule M, whereA is a separable and nuclear C*-algebra. We assume that the left A-action on the bimodule M is given in terms of compact module operators and that M is direct summand of the standard Hilbert module over A.
متن کاملThe Completely Bounded Approximation Property for Extended Cuntz–pimsner Algebras
The extended Cuntz–Pimsner algebra E(H), introduced by Pimsner, is constructed from a Hilbert B, B–bimodule H over a C∗–algebra B. In this paper we investigate the Haagerup invariant Λ(·) for these algebras, the main result being that Λ(E(H)) = Λ(B) when H is full over B. In particular, E(H) has the completely bounded approximation property if and only if the same is true for B.
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 2019
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-115634