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Extensions of AH algebras with the ideal property

Published online by Cambridge University Press:  20 January 2009

Cornel Pasnicu
Cornel Pasnicu
Affiliation:
Department of Mathematics and Computer Science, University of Puerto Rico, Box 23355, San Juan PR 00931-3355, U.S.A. E-mail address: [email protected]
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In this note we show that if we have an exact sequence of AH algebras (AH stands for “approximately homogeneous”) 0 → I → A → B → 0, then A has the ideal property (i.e., any ideal is generated by its projections) if and only if I and B have the ideal property. Also, we prove that an extension of two AT algebras (AT stands for “approximately circle”) with the ideal property is an AT algebra with the ideal property if and only if the extension is quasidiagonal.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 1 , February 1999 , pp. 65 - 76
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

REFERENCES

1.Brown, L. G., Extensions of AF algebras: the projection lifting problem (Proc. Sympos. Pure Math. 38, A.M.S., Providence, 1982).Google Scholar
2.Brown, L. G. and Dadarlat, M., Extensions of C*-algebras and quasidiagonality, J. London Math. Soc. (2), 53 (1996), 582–600.Google Scholar
3.Brown, L. G. and Pedersen, G. K., C*-aIgebras of real rank zero, J. Funct. Anal. 99 (1991), 131–149.Google Scholar
4.Dadarlat, M. and Eilers, S., Reducing torsion coefficient K-theory, preprint (preliminary version) (1996).Google Scholar
5.Dadarlat, M. and Loring, T. A., Extensions of certain real rank zero C*-algebras, preprint (1993).Google Scholar
6.Effros, E. G., Dimensions and C*-algebras (CBMS Regional Conf. Ser. in Math. 46, A.M.S., Providence, 1981).Google Scholar
7.Elliott, G. A., On the classification of C*-algebras of real rank zero, J. Reine Angew. Math. 443 (1993), 179–219.Google Scholar
8.Elliott, G. A., The classification problem for amenable C*-algebras, in Proceedings of the International Congress of Mathematicians, Zürich, Switzerland 1994 (Birkhäuser Verlag, Basel, Switzerland, 1995), 922–932.Google Scholar
9.Elliott, G. A. and Gong, G., On the classification of C*-algebras of real rank zero, II, Ann. of Math. 144 (1996), 497–610.CrossRefGoogle Scholar
10.Lin, H. and Rørdam, M., Extensions of inductive limits of circle algebras, J. London Math. Soc. (2), 51 (1995), 603–613.CrossRefGoogle Scholar
11.Murphy, G. J., Diagonality in C*-algebras, Math. Z. 199 (1988), 279–284.Google Scholar
12.Pasnicu, C., Shape equivalence, nonstable K-theory and AH algebras, preprint (1995).Google Scholar
13.Rieffel, M., Dimension and stable rank in the K-theory of C*-algebras, Proc. London Math. Soc. 46 (1983), 301–333.CrossRefGoogle Scholar
14.Stevens, K. H., The classification of certain non-simple approximate interval algebras (Ph.D. thesis, University of Toronto, 1994).Google Scholar
15.Zhang, S., K1-groups, quasidiagonality and interpolation by multiplier projections, Trans. Amer. Math. Soc. 325 (1991), 793–818.Google Scholar