Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Generalized Cuntz-Krieger algebras

Author(s): Valentin Deaconu
Journal: Proc. Amer. Math. Soc. 124 (1996), 3427-3435.
MSC (1991): Primary 46L05, 46L55, 46L80
MathSciNet review: 1343688
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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.

References:

[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 -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 -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 -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 -algebras, JOT 6 (1981), 125-133. MR 82m:46074
[Pi]: M.Pimsner, A class of -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 -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

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|