Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Residually finite dimensional and AF-embeddable $C^*$-algebras

Author: Huaxin Lin
Journal: Proc. Amer. Math. Soc. 129 (2001), 1689-1696
MSC (2000): Primary 46L05, 46L35
Published electronically: November 2, 2000
MathSciNet review: 1814098
Full-text PDF

Abstract | References | Similar Articles | Additional Information


We show that every separable nuclear residually finite dimensional $C^*$-algebras satisfying the Universal Coefficient Theorem can be embedded into a unital separable simple AF-algebra.

References [Enhancements On Off] (What's this?)

  • [BK1] B. Blackadar and E. Kirchberg Generalized inductive limits of finite-dimensional C*-algebras, Math. Ann. 307 (1997), 343-380. MR 98c:46112
  • [BK2] B. Blackadar and E. Kirchberg, Inner quasidiagonality and strong NF algebras, preprint.
  • [Br] N. P. Brown, AF embeddability of cross product of AF algebras by the integers, J. Funct. Anal. 160 (1998), 150-175. CMP 99:06
  • [D] M. Dadarlat, Residually finite dimensional $C^*$-algebras, Cont. Math., Amer. Math. Soc., 228 (1998), 45-50. MR 99m:46133
  • [DE] M. Dadarlat and S. Eilers, On the classification of nuclear $C^*$-algebras, preprint 1998.
  • [DL] M. Dadarlat and T. Loring, A universal multi-coefficient theorem for the Kasparov groups, Duke J. Math. 84 (1996), 355-377. MR 97f:46109
  • [Ell1] G. A. Elliott, On the classification of inductive limits of sequences of semi-simple finite dimensional algebras, J. Algebra 38 (1976), 29-44. MR 53:1279
  • [Ell2] G. A. Elliott, On the classification of $C^*$-algebras of real rank zero, J. Reine Angew. Math. 443 (1993), 179-219. MR 94i:46074
  • [GH] K. Goodearl and D. Handelman, Rank functions and $K_0$ of regular rings, J. Pure Appl. Algebra 7 (1976), 195-216. MR 52:10794
  • [K1] E. Kirchberg, On non-semisplit extensions, tensor products and exactness of group $C^*$-algebras, Invent. Math. 112 (1993), 449-489. MR 94d:46058
  • [Ln1] H. Lin Classification of simple $C^*$-algebras with unique traces, Amer. J. Math. 120 (1998), 1289-1315. CMP 99:04
  • [Ln2] H. Lin, Tracially AF $C^*$-algebras, Trans. Amer. Math. Soc., to appear.
  • [Ln3] H. Lin, Classification of simple TAF $C^*$-algebras, Can. J. Math., to appear.
  • [Pi] M. Pimsner, Embedding some transformation group $C^*$-algebras into AF algebras, Ergod. Th. Dynam. Sys. 3 (1983), 613-626. MR 86d:46054
  • [RS] J. Rosenberg and C. Schochet, The Kunneth theorem and the universal coefficient theorem for Kasparov's generalized functor, Duke Math. J. 55 (1987), 431-474. MR 88i:46091
  • [Sp] J. S. Spielberg, Embedding $C^*$-algebra extensions into AF-algebras, J. Funct. Anal. 81 (1988), 325-344. MR 90a:46154
  • [Vo] D. Voiculescu, Almost inductive limit automorphisms and embedding into AF-algebras, Ergod. Th. Dynam. Sys. 6 (1986), 475-484. MR 88k:46073

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46L05, 46L35

Retrieve articles in all journals with MSC (2000): 46L05, 46L35

Additional Information

Huaxin Lin
Affiliation: Department of Mathematics, East China Normal University, Shanghai, China
Address at time of publication: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222

Keywords: AF-embedding, TAF $C^*$-algebra
Received by editor(s): July 22, 1998
Received by editor(s) in revised form: September 13, 1999
Published electronically: November 2, 2000
Additional Notes: Research partially supported by NSF grants DMS 9801482
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society