## CONTINUOUS GRAPHS AND C*-ALGEBRAS (1998)

### BibTeX

@MISC{Deaconu98continuousgraphs,

author = {Valentin Deaconu},

title = {CONTINUOUS GRAPHS AND C*-ALGEBRAS},

year = {1998}

}

### OpenURL

### Abstract

We present the continuous graph approach for some generalizations of the Cuntz-Krieger algebras. These C*-algebras are simple, nuclear, and purely infinite, with rich K-theory. They are tied with the dynamics of a shift on an infinite path space. We explain the connection with the Ruelle algebras of Putnam, the Pimsner algebras, and the polymorphisms of Arzumanian and Renault.

### Citations

155 | Cuntz-Krieger algebras of directed graphs
- Kumjian, Pask, et al.
- 1998
(Show Context)
Citation Context .... This approach offers more freedom for constructing easy, concrete examples, with prescribed K-theory. It should be mentioned that C*-algebras associated with discrete graphs were studied in [KPRR], =-=[KPR]-=-, [KP]. See also the survey [K2]. The continuous graph approach is very similar to the point of view of polymorphisms or correspondences, introduced earlier in a measure theoretical context by Vershik... |

79 |
A class of C∗-algebras generalizing both Cuntz-Krieger algebras and crossed products by Z, Free probability theory
- Pimsner
- 1997
(Show Context)
Citation Context ...manian and Renault. 1991 Mathematics Subject Classification: Primary 46L05; Secondary 46L55 INTRODUCTION Recent papers are dealing with different generalizations of the Cuntz-Krieger algebras OA (see =-=[Pi]-=-, [P1], [D2], [AR], etc). The exact relationship between these approaches remains to be explored, but certainly there are overlaps. In [Pi], the author considers a Hilbert bimodule H over a C*-algebra... |

30 |
Automorphisms of compact groups
- Kitchens, Schmidt
- 1989
(Show Context)
Citation Context ...h l(i, j) = 0, this family is empty by definition. We take E to be the disjoint union of all the groups G ij k , 1 ≤ i, j ≤ N, 1 ≤ k ≤ l(i, j), with obvious origin and terminus maps. It is known (see =-=[KS]-=-) that there are families of d × d nonsingular matrices with integer entries, such that Aij = {A ij 1 , ..., A ij l(i,j) }, Bij = {B ij 1 , ..., B ij l(i,j) }. G ij l = {(z, w) ∈ Tdi × T d j | A ij l ... |

29 | Graphs, groupoids and Cuntz-Krieger algebras
- Kumjian, Pask, et al.
- 1997
(Show Context)
Citation Context ...K-theory. This approach offers more freedom for constructing easy, concrete examples, with prescribed K-theory. It should be mentioned that C*-algebras associated with discrete graphs were studied in =-=[KPRR]-=-, [KPR], [KP]. See also the survey [K2]. The continuous graph approach is very similar to the point of view of polymorphisms or correspondences, introduced earlier in a measure theoretical context by ... |

24 | Purely infinite C∗-algebras arising from dynamical systems - Anantharaman-Delaroche - 1997 |

24 |
C*-algebras from Smale spaces
- Putnam
- 1996
(Show Context)
Citation Context ... and Renault. 1991 Mathematics Subject Classification: Primary 46L05; Secondary 46L55 INTRODUCTION Recent papers are dealing with different generalizations of the Cuntz-Krieger algebras OA (see [Pi], =-=[P1]-=-, [D2], [AR], etc). The exact relationship between these approaches remains to be explored, but certainly there are overlaps. In [Pi], the author considers a Hilbert bimodule H over a C*-algebra, and ... |

18 | Fell bundles over groupoids
- Kumjian
- 1998
(Show Context)
Citation Context ...ted to isomorphic Fell bundles over the group Z. This point of view was suggested by Abadie, Eilers and Exel in [AEE]. The definition of a Fell bundle and of the associated C ∗ -algebra is taken from =-=[K1]-=-. To the pair (H∞, FH), we can associate the Fell bundle B, where Bn := H ⊗n ∞ , n ∈ Z. The multiplication is given by the tensor product, identifying H ∗ ∞ ⊗ H∞ with FH and H∞ ⊗ H ∗ ∞ with the ideal ... |

16 | D.: C∗-algebras of directed graphs and group actions. Ergod. Theory Dyn
- Kumjian, Pask
- 1999
(Show Context)
Citation Context ...approach offers more freedom for constructing easy, concrete examples, with prescribed K-theory. It should be mentioned that C*-algebras associated with discrete graphs were studied in [KPRR], [KPR], =-=[KP]-=-. See also the survey [K2]. The continuous graph approach is very similar to the point of view of polymorphisms or correspondences, introduced earlier in a measure theoretical context by Vershik and A... |

15 | Generalized Cuntz-Krieger algebras
- Deaconu
- 1996
(Show Context)
Citation Context ...enault. 1991 Mathematics Subject Classification: Primary 46L05; Secondary 46L55 INTRODUCTION Recent papers are dealing with different generalizations of the Cuntz-Krieger algebras OA (see [Pi], [P1], =-=[D2]-=-, [AR], etc). The exact relationship between these approaches remains to be explored, but certainly there are overlaps. In [Pi], the author considers a Hilbert bimodule H over a C*-algebra, and creati... |

8 | Operator algebras and hyperbolic dynamics, Operator Algebras and Quantum Field Theory, Editors - Kaminker, Putnam, et al. - 1997 |

7 |
Examples of pseudogroups and their C*-algebras, in ‘Operator Algebras and Quantum Field Theory’, Editors
- Arzumanian, Renault
- 1997
(Show Context)
Citation Context .... 1991 Mathematics Subject Classification: Primary 46L05; Secondary 46L55 INTRODUCTION Recent papers are dealing with different generalizations of the Cuntz-Krieger algebras OA (see [Pi], [P1], [D2], =-=[AR]-=-, etc). The exact relationship between these approaches remains to be explored, but certainly there are overlaps. In [Pi], the author considers a Hilbert bimodule H over a C*-algebra, and creation ope... |

7 |
Notes on C∗-algebras of graphs
- Kumjian
- 1998
(Show Context)
Citation Context ...om for constructing easy, concrete examples, with prescribed K-theory. It should be mentioned that C*-algebras associated with discrete graphs were studied in [KPRR], [KPR], [KP]. See also the survey =-=[K2]-=-. The continuous graph approach is very similar to the point of view of polymorphisms or correspondences, introduced earlier in a measure theoretical context by Vershik and Arzumanian (see [AR] for a ... |

6 | Groupoids associated with endomorphisms, Trans - Deaconu - 1995 |

6 |
Entropy of graphs, semigroups and groups
- Friedland
- 1996
(Show Context)
Citation Context ...cal system (X+, σ+) unifies in a natural way the notion of a covering map T : V → V , a (finitely-generated) semigroup or group of covering maps S : V → V and the (unilateral) Markov shifts (see also =-=[F]-=-). It has the advantage that we get a single local homeomorphism. Example 1 will produce the unilateral and bilateral Markov shifts. In general, we may think that we have a “continuous” set of symbols... |

2 | Hilbert C∗-bimodules and continuous Cuntz-Krieger algebras considered by Deaconu - Kajiwara, Watatani |