Stable rank of inclusion of C*-algebras of depth 2

الأصل · EN

Let 1 ∈ A ⊂ B be an inclusion of unital C*-algebras of index-finite type and depth 2. Suppose that A is infinite dimensional simple with tsr(A) = 1 and SP-property. Then tsr(B) ≤ 2. As a corollary when A is a simple C*-algebra with (A) = 1 and SP-property and α an action of a finite group G on (A), (A αG) ≤ 2.