Mathematical Sciences: K-Theory of Crossed Products of C*-Algebras by Locally Compact Groups

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9401592 McClanahan The investigator has previously shown that Pimsner's most general exact sequence of K-groups is valid in the case of twisted crossed products relative to a circle 2-valued cocycle. One component of the proposed project involves extending this result to the case of unitary multiplier-valued cocycles. A possible application of this result would be the computation of the K-groups of certain group C*-algebras in terms of the K- groups of the group C*-algebras of a normal subgroup and of an action of the corresponding quotient group. The investigator plans to investigate extending Pimsner's exact sequence for groups acting on trees to the partial crossed product setting. This will enable the computation of the K-groups of many other amalgamated products of C*-algebras. This project involves computation of invariants of operator algebras. An operator is an infinite dimensional generalization of matrices. Given the natural algebraic structure a collection of operators can frequently be considered as an algebra. A C*-algebra is an algebra of operators with additional topological structure that is closed under the adjoint operation. A basic problem is to classify operator algebras up to isomorphism. This is frequently handled by determining simple invariants associated with operator algebras. One such invariant is the K-group of a C*-algebra. This project will provide explicit computations of K-groups of product C*-algebras. ***