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Extremal K -Theory and Index for C*-Algebras
Authors:Lawrence G Brown and Gert K Pedersen
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
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.
Keywords:K-theory  extremally rich C *-algebras  index theory
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