Extremal K -Theory and Index for C*-Algebras |
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Authors: | Lawrence G Brown and Gert K Pedersen |
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Institution: | (1) Department of Mathematics, Purdue University, West Lafayette, Indiana, 47906, U.S.A.;(2) Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark |
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Abstract: | We develop the general theory for a new functor K
e on the category of C
*-algebras. The extremal K-set, K
e
(A), of a C
*-algebra A is defined by means of homotopy classes of extreme partial isometries. It contains K
1
(A) and admits a partially defined addition extending the addition in K
1
(A), so that we have an action of K
1
(A) on K
e
(A). We show how this functor relates to K
0 and K
1, and how it can be used as a carrier of information relating the various K-groups of ideals and quotients of A. The extremal K-set is then used to extend the classical theory of index for Fredholm and semi-Fredholm operators. |
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Keywords: | K-theory extremally rich C
*-algebras index theory |
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