$C^*$-Crossed-Products by an Order-Two Automorphism

Canadian mathematical bulletin

关键词: $alpha$-Bloch function;    multiplication operator;   

DOI  :  10.4153/CMB-2010-008-4

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We describe the representation theory of $C^*$-crossed-products of a unital $C^*$-algebra A by the cyclic group of order~2. We prove that there are two main types of irreducible representations for the crossed-product: those whose restriction to A is irreducible and those who are the sum of two unitarily unequivalent representations of~A. We characterize each class in term of the restriction of the representations to the fixed point $C^*$-subalgebra of~A. We apply our results to compute the K-theory of several crossed-products of the free group on two generators.

【 授权许可】

Unknown