Endomorphisms of stable continuous-trace $C^*$-algebras
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- by Ilan Hirshberg
- Proc. Amer. Math. Soc. 132 (2004), 481-486
- DOI: https://doi.org/10.1090/S0002-9939-03-07115-6
- Published electronically: July 31, 2003
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Abstract:
We classify $C_0(X)$-endomorphisms of stable continuous-trace $C^\ast$-algebras up to inner automorphism by a surjective multiplicative invariant taking values in finite-dimensional vector bundles over the spectrum. Specializing to automorphisms, this gives a different approach to results of Lance, Smith, Phillips and Raeburn.References
- Jacques Dixmier, $C^*$-algebras, North-Holland Mathematical Library, Vol. 15, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. Translated from the French by Francis Jellett. MR 0458185
- Albrecht Dold, Partitions of unity in the theory of fibrations, Ann. of Math. (2) 78 (1963), 223–255. MR 155330, DOI 10.2307/1970341
- Max Karoubi, $K$-theory, Grundlehren der Mathematischen Wissenschaften, Band 226, Springer-Verlag, Berlin-New York, 1978. An introduction. MR 0488029
- E. C. Lance, Automorphisms of certain operator algebras, Amer. J. Math. 91 (1969), 160–174. MR 241989, DOI 10.2307/2373275
- John Phillips and Iain Raeburn, Automorphisms of $C^{\ast }$-algebras and second Čech cohomology, Indiana Univ. Math. J. 29 (1980), no. 6, 799–822. MR 589649, DOI 10.1512/iumj.1980.29.29058
- Geoffrey L. Price, Endomorphisms of certain operator algebras, Publ. Res. Inst. Math. Sci. 25 (1989), no. 1, 45–57. MR 999349, DOI 10.2977/prims/1195173761
- Iain Raeburn and Dana P. Williams, Morita equivalence and continuous-trace $C^*$-algebras, Mathematical Surveys and Monographs, vol. 60, American Mathematical Society, Providence, RI, 1998. MR 1634408, DOI 10.1090/surv/060
- Jonathan Rosenberg, Continuous-trace algebras from the bundle theoretic point of view, J. Austral. Math. Soc. Ser. A 47 (1989), no. 3, 368–381. MR 1018964, DOI 10.1017/S1446788700033097
- Mi-soo Bae Smith, On automorphism groups of $C^*$-algebras, Trans. Amer. Math. Soc. 152 (1970), 623–648. MR 273426, DOI 10.1090/S0002-9947-1970-0273426-2
Bibliographic Information
- Ilan Hirshberg
- Affiliation: Department of Mathematics, University of California at Berkeley, Berkeley, California 94720
- Email: ilan@math.berkeley.edu
- Received by editor(s): February 1, 2002
- Received by editor(s) in revised form: October 10, 2002
- Published electronically: July 31, 2003
- Communicated by: David R. Larson
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 481-486
- MSC (2000): Primary 46L05, 46M20
- DOI: https://doi.org/10.1090/S0002-9939-03-07115-6
- MathSciNet review: 2022372