Cuntz-Pimsner $C*$-Algebras and Crossed Products by Hilbert $C*$-Bimodules
نویسندگان
چکیده
منابع مشابه
On Approximation Properties of Pimsner Algebras and Crossed Products by Hilbert Bimodules
Let X be a Hilbert bimodule over a C-algebra A and OX = A ⋊X Z. Using a finite section method we construct a sequence of completely positive contractions factoring through matrix algebras over A which act on sξs ∗ η as Schur multipliers converging to the identity. This shows immediately that for a finitely generated X the algebra OX inherits any standard approximation property such as nuclearit...
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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...
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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 کاملGauge-equivariant Hilbert bimodules and crossed products by endomorphisms
C*-algebra endomorphisms arising from superselection structures with non-trivial centre define a ’rank’ and a ’first Chern class’. Crossed products by such endomorphisms involve the Cuntz-Pimsner algebra of a vector bundle having the above-mentioned rank and first Chern class, and can be used to construct a duality for abstract (nonsymmetric) tensor categories vs. group bundles acting on (nonsy...
متن کاملFull Crossed Products by Hopf C∗-algebras
We show that when a co-involutive Hopf C *-algebra S coacts via δ on a C *-algebra A, there exists a full crossed product A × δ S, with universal properties analogous to those of full crossed products by locally compact groups. The dual Hopf C *-algebra is then defined byˆS := C × id S.
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2009
ISSN: 0035-7596
DOI: 10.1216/rmj-2009-39-4-1051