Cuntz-Krieger-Pimsner algebras associated with amalgamated free product groups

@article{Okayasu2000CuntzKriegerPimsnerAA,
  title={Cuntz-Krieger-Pimsner algebras associated with amalgamated free product groups},
  author={Rui Okayasu},
  journal={Publications of The Research Institute for Mathematical Sciences},
  year={2000},
  volume={38},
  pages={147-190}
}
  • Rui Okayasu
  • Published 10 October 2000
  • Mathematics
  • Publications of The Research Institute for Mathematical Sciences
We give a construction of a nuclear C*-algebra associated with an amalgamated free product of groups, generalizing Spielberg's construction of a certain Cuntz-Krieger algebra associated with a finitely generated free product of cyclic groups. Our nuclear C*-algebras can be identified with certain Cuntz-Krieger-Pimsner algebras. We will also show that our algebras can be obtained by the crossed product construction of the canonical actions on the hyperbolic boundaries, which proves a special… 
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References

SHOWING 1-10 OF 46 REFERENCES
FREE-PRODUCT GROUPS, CUNTZ-KRIEGER ALGEBRAS, AND COVARIANT MAPS
A construction is given relating a finitely generated free-product of cyclic groups with a certain Cuntz-Krieger algebra, generalizing the relation between the Choi algebra and 02. It is shown that a
Purely infinite C*-algebras from boundary actions of discrete groups.
There are various examples of dynamical Systems giving rise to simple C*-algebras, in which hyperbolicity, or a weakened form thereof, precludes the existence of a trace. In these situations one
EXACTNESS OF CUNTZ–PIMSNER C*-ALGEBRAS
Abstract 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
On Subalgebras of the Car-Algebra
Abstract Every nuclear unital separable C *-algebra A is unitally and completely isometrically ismorphic to the range of a unital completely positive projection on the CAR-algbra B = M 2 ⊗ M 2 ⊗ ···.
SimpleC*-algebra generated by isometries
AbstractWe consider theC*-algebra $$\mathcal{O}_n $$ generated byn≧2 isometriesS1,...,Sn on an infinite-dimensional Hilbert space, with the property thatS1S*1+...+SnS*n=1. It turns out that
Faithful representations of crossed products by endomorphisms
Stacey has recently characterised the crossed product A x, N of a C*-algebra A by an endomorphism a as a C*-algebra whose representations are given by covariant representations of the system (A, a) .
A Simple C*-Algebra Generated by Two Finite-Order Unitaries
We present an example which illustrates several peculiar phenomena that may occur in the theory of C*-algebras. In particular, we show that a C*-subalgebra of a nuclear (amenable) C*-algebra need not
Infinite simple C*-algebras and Reduced cross products of abelian C*-algebras and free groups
SummaryLet Γ=〈g1〉*〈g2〉*...*〈gn〉*... be a free product of cyclic groups with generators {gi}, andCr* (Γ,℘Λ) be the C*-algebra generated by the reduced group C*-algebraCr*Γ and a set of projectionsPgL
$C^*$--algebras arising from group actions on the boundary of a triangle building
A subgroup of an amenable group is amenable. The $C^*$-algebra version of this fact is false. This was first proved by M.-D. Choi who proved that the non-nuclear $C^*$-algebra $C^*_r(\ZZ_2*\ZZ_3)$ is
Crossed products of C*-algebras by endomorphisms
The concept of a twisted crossed product associated to a non-classical C*-dynamical system is introduced and studied. The relationship between a covariant projective representation of the system and
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