Inclusions of Simple C-algebras
نویسنده
چکیده
We prove that if a conditional expectation from a simple C∗-algebra onto its C∗-subalgebra satisfies the Pimsner-Popa inequality, there exists a quasibasis. As an application, we establish the Galois correspondence for outer actions of finite groups (and more generally finite dimensional Kac algebras) on simple C∗algebras. We also introduce the notion of sectors for stable simple C∗-algebras and purely infinite simple C∗-algebras in the Cuntz standard form, and discuss several applications, including their relationship to K-theory.
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