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Generalized Cuntz-Krieger algebras

Author: Valentin Deaconu
Journal: Proc. Amer. Math. Soc. 124 (1996), 3427-3435
MSC (1991): Primary 46L05, 46L55, 46L80
MathSciNet review: 1343688
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Abstract: To a special embedding $\Phi $ of circle algebras having the same spectrum, we associate an r-discrete, locally compact groupoid, similar to the Cuntz-Krieger groupoid. Its $\mathbf {C}^*$-algebra, denoted $\mathcal {O}_{\Phi }$, is a continuous version of the Cuntz-Krieger algebras $\mathcal {O}_A$. The algebra $\mathcal {O}_{\Phi }$ is generated by an AT-algebra and a nonunitary isometry. We compute its K-theory under the assumption that the AT-algebra is simple.

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  • [Bl] B. Blackadar, Symmetries of the CAR algebra, Annals of Math. 131(1990) 589-623. MR 91i:46084
  • [Br1] O.Bratteli, Inductive limits of finite dimensional $C^*$-algebras, Trans. of the AMS 171 (1972) 195-234. MR 47:844
  • [Cu] J.Cuntz, A Class of $\mathbf {C}^*$-algebras and Topological Markov Chains II: Reducible Chains and the Ext-functor for $\mathbf {C}^*$-algebras , Invent. Math. 63(1981) 25-40. MR 82f:46073
  • [Da] M.D\u{a}dârlat, On homomorphisms of certain $C^*$-algebras, INCREST Preprint Series No.11, 1986.
  • [De1] V.Deaconu, Groupoids associated with endomorphisms , Trans. of the AMS 347(1995) 1779-1786. MR 95h:46104
  • [De2] V.Deaconu, A Path Model for Circle Algebras, J. Operator Theory 34(1995), 57-89. CMP 96:04
  • [Ku] A.Kumjian, Preliminary algebras arising from local homeomorphisms, Math.Scand. vol 52(1983), 269-278. MR 85b:46078
  • [Mu] P.S.Muhly, Coordinates in Operator Algebra, to appear.
  • [MRS] M.H. Mann, I. Raeburn, C.E. Sutherland, Representations of compact groups, Cuntz-Krieger algebras, and groupoid $\mathbf {C}^*$-algebras, Miniconf. Probab. Anal. (Sydney, 1991), Proc. Centre Math., vol. 29, Australian Nat. Univ., Canberra, 1992, pp. 135--144. MR 93m:46082
  • [MRW] P.S.Muhly, J.Renault, D.P.Williams, Equivalence and isomorphism for groupoid $\mathbf {C}^*$-algebras, JOT 17(1987) 3-22. MR 88h:46123
  • [Pa1] W.L. Paschke,The crossed product of a $C^*$-algebra by an endomorphism, Proc. Amer. Math. Soc.80(1980), 113-118. MR 81m:46081
  • [Pa2] W.L. Paschke,K-theory for actions of the circle group on $C^*$-algebras, JOT 6 (1981), 125-133. MR 82m:46074
  • [Pi] M.Pimsner, A class of $C^*$-algebras generalizing both Cuntz-Krieger algebras and crossed products by Z, Preprint 1993.
  • [Pu] I.F.Putnam, $\mathbf {C}^*$-algebras from Smale spaces, Canadian J. of Math. 48 (1996), No. 1, 175--195.
  • [Re] J.Renault, A groupoid approach to $\mathbf {C}^*$-algebras, Springer Lecture Notes in Math., no.793, Springer-Verlag, Berlin, 1980. MR 82h:46075
  • [Rø] M.Rørdam, Classification of Certain Infinite Simple $ C^*$-algebras, III, Preprint 1994.
  • [Th] K.Thomsen, Homomorphisms between finite direct sums of circle algebras, Linear and Multilinear Algebra 32(1992) 33-50. MR 94a:46080

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Additional Information

Valentin Deaconu
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Address at time of publication: Department of Mathematics, Iowa State University, Ames, Iowa 50011

Received by editor(s): May 15, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

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