Proceedings of the American Mathematical Society

Author(s): D. Drinen
Journal: Proc. Amer. Math. Soc. 128 (2000), 1991-2000.
MSC (1991): Primary 46L05; Secondary 22A22
Posted: November 1, 1999
Retrieve article in: PDF
This article is available free of charge

Abstract: Every AF-algebra

arises as the

-algebra of a locally finite pointed directed graph in the sense of Kumjian, Pask, Raeburn, and Renault. For AF-algebras, the diagonal subalgebra defined by Stratila and Voiculescu is consistent with Kumjian's notion of diagonal, and the groupoid arising from a well-chosen Bratteli diagram for

coincides with Kumjian's twist groupoid constructed from a diagonal of

1.: C. Anantharaman-Delaroche and J. Renault, Amenable groupoids, Mem. Amer. Math. Soc., (to appear).
2.: O. Bratteli, Inductive limits of finite dimensional ${C}^*$ -algebras, Trans. Amer. Math. Soc. 171 (1972), 195-234. MR 47:844
3.: E. Effros, Dimensions and ${C}^*$ -algebras, CBMS Regional Conf. Ser. in Math. no. 46, American Mathematical Society, Providence, RI, 1980. MR 84k:46042
4.: A. Kumjian, On ${C}^*$ -diagonals, Can. J. Math. 38 (1986), 969-1008. MR 88a:46060
5.: A. Kumjian, D. Pask, and I. Raeburn, Cuntz-Krieger algebras of directed graphs, Pacific J. Math. 184 (1998), 161-174. CMP 98:13
6.: A. Kumjian, D. Pask, I. Raeburn, and J. Renault, Graphs, groupoids, and Cuntz-Krieger algebras, J. Funct. Anal. 144 (1997), 505-541. MR 98g:46083
7.: S.C. Power, Limit algebras, Pitman Research Notes in Mathematics, vol. 278, Longman Scientific and Technical, London, 1992. MR 94g:46001
8.: J. N. Renault, A groupoid approach to ${C}^*$ -algebras, Lecture Notes in Math., no. 793, Springer-Verlag, New York, 1980. MR 92h:46075
9.: S. Str[??]atil[??]a and D. Voiculescu, Representations of AF-algebras and of the group ${U}(\infty)$ , Lecture Notes in Math., no. 486, Springer, New York, 1975. MR 56:16391

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46L05, 22A22

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

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS