# 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} }

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…

## 7 Citations

Type III factors arising from Cuntz-Krieger algebras

- Mathematics
- 2002

We determine the types of factors arising from GNS-representations of quasi-free KMS states on Cuntz-Krieger algebras. Applying our result to the Cuntz-Krieger algebras arising from the boundary…

Bass--Serre trees of amalgamated free product C*-algebras

- Mathematics
- 2016

For any reduced amalgamated free product $\mathrm{C}^*$-algebra $(A,E)=(A_1, E_1) \ast_D (A_2,E_2)$, we introduce and study a canonical ambient $\mathrm{C}^*$-algebra $\Delta\mathbf{T}(A,E)$ of $A$…

Amenable minimal Cantor systems of free groups arising from diagonal actions

- Mathematics
- 2017

We study amenable minimal Cantor systems of free groups arising from the diagonal actions of the boundary actions and certain Cantor systems. It is shown that every virtually free group admits…

Random walks on groups and KMS states

- Mathematics
- 2020

A classical construction associates to a transient random walk on a discrete group $\Gamma$ a compact $\Gamma$-space $\partial_M \Gamma$ known as the Martin boundary. The resulting crossed product…

Entropy of subshifts and the Macaev norm

- Mathematics
- 2004

We obtain the exact value of Voiculescu's invariant k �ðtÞ, which is an obstruction of the existence of quasicentral approximate units relative to the Macaev ideal in perturbation theory, for a tuple…

Topological full groups of one-sided shifts of finite type

- Mathematics
- 2012

We explore the topological full group [[G]] of an essentially principal etale groupoid G on a Cantor set. When G is minimal, we show that [[G]] (and its certain normal subgroup) is a complete…

Noncommutative Bass-Serre trees and their applications

- Mathematics
- 2017

Any amalgamated free product of discrete groups acts on its associated Bass–Serre tree. In this paper, we consider an analogue of the Bass–Serre trees for reduced amalgamated free products of…

## References

SHOWING 1-10 OF 46 REFERENCES

FREE-PRODUCT GROUPS, CUNTZ-KRIEGER ALGEBRAS, AND COVARIANT MAPS

- Mathematics
- 1991

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.

- Mathematics
- 1996

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

- MathematicsProceedings of the Edinburgh Mathematical Society
- 2001

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

- Mathematics
- 1995

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

- Mathematics
- 1977

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

- Mathematics
- 1993

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

- MathematicsCanadian Journal of Mathematics
- 1979

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

- Mathematics
- 1997

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

- Mathematics
- 1996

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

- Mathematics
- 1996

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…