The K-theory of crossed products
Crossed products for group actions yield many interesting C*-algebras. First we consider the case of crossed products by ℤ. Their K-theory is computed by the Pimsner-Voiculescu exact sequence . We use crossed Toeplitz algebras to get it, following . For crossed products by more general groups, there is a good guess for what the K-theory ought to be: this is the celebrated Baum-Connes conjecture. We discuss an alternative formulation of this conjecture, which is once again based on Toeplitz algebras.
KeywordsExact Sequence Compact Group Banach Algebra Compact Subgroup Compact Open Subgroup
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