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On ext(G2)

Part of: Methods of category theory in functional analysis

Published online by Cambridge University Press:  26 February 2010

Victor Snaith
Victor Snaith
Affiliation:
Department of Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B9.
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Extract

In [7[ a functor Ext is defined in terms of C*-extensions. It is a covariant functor from the homotopy category of compact, metrizable spaces to abelian groups. Further details are given in [7, 8, 9, 11]. From [7, 14] Ext extends to a Steenrod homology theory, Ext*, which may be identified with the one associated with unitary K-theory. Since Lie groups are fundamental to K-theory (see [2, p. 24]) one might expect Ext(G) to be of interest when G is a Lie group.

MSC classification

Secondary: 46M20: Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
Type
Research Article
Information
Mathematika , Volume 28 , Issue 1 , June 1981 , pp. 79 - 85
Copyright
Copyright © University College London 1981

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References

1.Adams, J. F.. Lectures on Lie Groups (Benjamin, New York, 1969).Google Scholar
2.Atiyah, M. F.. K-Theory (Benjamin, New York, 1967).Google Scholar
3.Atiyah, M. F.. “On the K-Theory of compact Lie groups”, Topology, 4 (1965), 95–99.Google Scholar
4.Atiyah, M. F.. “Vector bundles and the Kunneth formula”, Topology, 1 (1963), 245–248.CrossRefGoogle Scholar
5.Borel, A.. “Kahlerian coset spaces of semi-simple Lie groups”, Proc. Acad. Nat. Sci., 40 (1954), 1147–1151.Google Scholar
6.Borel, A.. Linear Algebraic Groups (Benjamin, New York, 1969).Google Scholar
7.Brown, L. G., Douglas, R. G. and Fillmore, P. A.. “Extensions of C*-algebras and K-homology”, Annals of Math., 105 (1977), 265–324.CrossRefGoogle Scholar
8.Brown, L. G., Douglas, R. G. and Fillmore, P. A.. “Unitary equivalence modulo the compact operators and extensions of C*-algebras”, Proc. Con), on Operator Theory, Lecture Notes in Mathematics, 345 (Springer-Verlag, Heidelberg, 1973).Google Scholar
9.Davie, A. M.. “Classification of essential normal operators, space of analytic functions”, Lecture Notes in Mathematics, 512 (Springer-Verlag, Heidelberg, 1975).Google Scholar
10.Dixmier, J.. Les C*-algçbres et leurs representations (Gauthier-Villars, Paris, 1969).Google Scholar
11.Douglas, R. G.. “Extensions of C*-algebras and K-homology”, Proc. Conf. on K-theory and Operator Algebras, Lecture Notes in Mathematics, 575 (Springer-Verlag, Heidelberg, 1977).Google Scholar
12.Gray, B.. Homotopy Theory, An Introduction to Algebraic Topology (Academic Press, New York, 1975).Google Scholar
13.Hodgkin, L.. “On the K-theory of Lie groups”, Topology, 6 (1967), 1–36.Google Scholar
14.Kahn, D. S., Kaminker, J. and Schochet, C.. “Generalised homology theories on compact metric spaces”, Michigan J. Math., 24 (1977), 203–224.CrossRefGoogle Scholar
15.Serre, J.-P.. Algebres de Lie semi-simples complexes (Benjamin, New York, 1966).Google Scholar
16.Snaith, V. P.. “On the K-theory of homogeneous spaces and conjugate bundles of Lie groups”, Proc. London Math. Soc. (3), 22 (1971), 562–584.CrossRefGoogle Scholar
17.Steinberg, R.. “On a theorem of Pittie”, Topology, 14 (1975), 173–177.CrossRefGoogle Scholar