Dimension and stable rank in the K-theory of C*-algebras

Proceedings of the London Mathematical Society

Volumn S3-46, Issue 2, 1983, Pages 301-333

  Rieffel, Marc A ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646873414     PISSN: 00246115     EISSN: 1460244X     Source Type: Journal    
DOI: 10.1112/plms/s3-46.2.301     Document Type: Article

References (51)

1. H. BASS, ‘K-theory and stable algebra’, Publications Mathématiques 22 (Institut des Hautes Études Scientifiques, Paris, 1964), pp. 489-544.
2. H. BASS, Algebraic K-theory (Benjamin, New York, 1968).
3. H. BASS, Introduction to some methods of algebraic K-theory, Conference Board Math. Sci. 20 (American Mathematical Society, Providence, R.I., 1974).
4. B. BLACKADAR and D. HANDELMAN, ‘Dimension functions and traces on C*-algebras’, J. Fund. Anal., 45 (1982), 297-340.
5. O. BRATTELI, ‘The center of approximately finite-dimensional C*-algebras’, J. Fund. Anal., 21 (1976), 195-202.
6. L. G. BROWN, P. GREEN, and M. A. RIEFFEL, ‘Stable isomorphism and strong Morita equivalence of C*-algebras’, Pacific J. Math., 71 (1977), 349-363.
7. J. W. BUNCE AND J. A. DEDDENS, ‘A family of simple C*-algebras related to weighted shift operators’, J. Fund. Anal., 19 (1974), 13-24.
8. J. CUNTZ, ‘Simple C*-algebras generated by isometries’, Comm. Math. Phys., 57 (1977), 173-185.
9. R. G. DOUGLAS, Banach algebra techniques in operator theory (Academic Press, New York, 1972).
10. E. G. EFFROS, Dimensions and C*-algebras, Conference Board Math. Sci. 46 (American Mathematical Society, Providence, R.I., 1981).
11. G. A. ELLIOTT, ‘On the /v-theory of the C*-algebra generated by a projective representation of a torsion-free abelian group’, Proceedings conference on operator algebras and group representations, Neptune, Romania, 1980 (Pitman, London, to appear).
12. P. GREEN, ‘C*-algebras of transformation groups with smooth orbit space’, Pacific J. Math., 72 (1977), 71-97.
13. P. GREEN, ‘The local structure of twisted covariance algebras’, Acta Math., 140 (1978), 191-250.
14. D. HANDELMAN, ‘Stable range in AW* algebras’, Proc. Amer. Math. Soc., 76 (1979), 241-249.
15. W. HUREWITZ, ‘Sur la dimension des produits Cartésiens’, Ann. of Math., 36 (1935), 194-197.
16. W. HUREWITZ and H. WALLMAN, Dimension theory (Princeton University Press, 1941).
17. D. HUSEMOLLER, Fibre bundles (McGraw-Hill, New York, 1966).
18. 1-an introduction to algebraic C*-theory’, Amer. Math. Monthly, 82 (1975), 329-364.
19. J. MILNOR, Introduction to algebraic K-theory, Annals of Mathematics Studies 72 (Princeton University Press, Princeton, 1971).
20. J. NAGATA, Modern dimension theory (North-Holland, Amsterdam, 1965).
21. W. L. PASCHKE, ‘Inner product modules over B*-algebras’, Trans. Amer. Math. Soc., 182 (1973), 443-468.
22. A. R. PEARS, Dimension theory of general spaces (Cambridge University Press, 1975).
23. G. K. PEDERSEN, C*-algebras and their automorphism groups, London Mathematical Society Mono graphs 14 (Academic Press, London, 1979).
24. L. S. PONTRYAGIN, ‘Sur une hypothèse fondamentale de la théorie de la dimension’, C. R. Acad. Sci. Paris Ser. A-B, 190(1930), 1105-1107.
25. C. E. RICKART, General theory of Banach algebras (Van Nostrand, Princeton, 1960).
26. M. A. RIEFFEL, ‘On the uniqueness of the Heisenberg commutation relations’, Duke Math. J., 39 (1972), 745-752.
27. M. A. RIEFFEL, ‘Induced representations of C*-algebras’, Adv. in Math., 13 (1974), 176-257.
28. M. A. RIEFFEL, ‘Morita equivalence for C*-algebras and W*-algebras’, J. Pure Appl. Algebra, 5 (1974), 51-96.
29. M. A. RIEFFEL, ‘Unitary representations of group extensions; an algebraic approach to the theory of Mackey and Blattner’, Studies in analysis, Advances in Mathematics Supplementary Studies 4 (Academic Press, New York, 1979), pp. 43-82.
30. M. A. RIEFFEL, ‘C*-algebras associated with irrational rotations’, Pacific J. Math., 93 (1981), 415-429.
31. M. A. RIEFFEL, ‘Morita equivalence for operator algebras’, Operator algebras and applications (ed. R. V. Kadison), Proceedings Symposia in Pure Mathematics 38 (American Mathematical Society, Providence, 1982), pp. 285-298.
32. A. G. ROBERTSON, ‘On the density of the invertible group in C*-algebras’, Proc. Edinburqh Math. Soc., 20 (1976), 153-157.
33. A. G. ROBERTSON, ‘Stable range in C*-algebras’, Math. Proc. Cambridge Philos. Soc., 87 (1980), 413-418.
34. J. ROSENBERG, ‘The C*-algebras of some real and p-adic solvable groups’, Pacific J. Math., 65 (1967), 174-192.
35. J. ROSENBERG, ‘Homological invariants of extensions of C*-algebras’, Operator algebras and applications (ed. R. V. Kadison), Proceedings Symposia in Pure Mathematics 38 (American Mathematical Society, Providence, 1982), pp. 35-75.
36. J. ROSENBERG, ‘C*-algebras and topological invariants’, Proceedings conference on operator algebras and group representations, Neptune, Romania, 1980 (Pitman, London, to appear).
37. J. ROSENBERG, ‘The role of /¿-theory in non-commutative algebraic topology’, Contemporary Math., 10 (1982), 155-182.
38. L. A. RUBEL, ‘Solution to problem 6117', Amer. Math. Monthly, 85 (1978), 505-506.
39. 2and related functions modeled on Chevalley groups’, Japanese J. Math., 4 (1978), 77-108.
40. R. SWAN, ‘Vector bundles and projective modules’, Trans. Amer. Math. Soc., 105 (1962), 264-277.
41. J. L. TAYLOR, ‘Banach algebras and topology’, Algebras in analysis (ed. J. H. Williamson, Academic Press, New York, 1975), pp. 118-186.
42. L. N. VASERSTEIN, ‘On the stabilization of the general linear group over a ring’, Math. USSR-Sb., 8 (1969), 383-400.
43. L. N. VASERSTEIN, ‘Stable rank of rings and dimensionality of topological spaces’, Functional Anal. Appi., 5 (1971), 102-110.
44. R. B. WARFIELD, JR., ‘Stable equivalence of matrices and resolutions’, Comm. Algebra, 6 (1978), 1811-1828.
45. R. B. WARFIELD, JR., ‘Stable generation of modules’, Lecture Notes in Mathematics 700 (Springer, Berlin, 1979), pp. 16-33.
46. R. B. WARFIELD, JR., ‘Modules over fully bounded Noetherian rings’, Lecture Notes in Mathematics 734 (Springer, Berlin, 1979), pp. 339-352.
47. R. B. WARFIELD, JR., ‘Cancellation of modules and groups and stable range of endomorphism rings’, Pacific J. Math., 91 (1980), 457-485.
48. R. B. WARFIELD, JR., ‘The number of generators of a module over a fully bounded ring’, J. Algebra, 66 (1980), 425-447.
49. A. V. ZARELUA, ‘On the extension of mappings to bicompactifications preserving some special properties’, Sibirsk. Mat. Z., 5 (1964), 532-548 (in Russian).
50. D. N. Z’EP, ‘Structure of the group C*-algebra of the group of affine transformations of a straight line’, Functional Anal. Appi., 9 (1975), 58-60.
51. M. A. RIEFFEL, ‘The cancellation theorem for projective modules over irrational rotation C’-algebras’, Proc. London Math. Soc. (3), 47 (1983), to appear.