Let A ∊ M n (ℝ) be an invertible matrix. Consider the semi-direct product ℝ n ⋊ ℤ where the action of ℤ on ℝ n is induced by the left multiplication by A. Let (α, τ) be a strongly continuous action of ℝn ⋊ ℤ on a C*-algebra B where α is a strongly continuous action of ℝn and τ is an automorphism. The map τ induces a map . We show that, at the K-theory level, τ commutes with the Connes–Thom map if det(A) > 0 and anticommutes if det(A) < 0. As an application, we recompute the K-groups of the Cuntz–Li algebra associated with an integer dilation matrix.
Email your librarian or administrator to recommend adding this journal to your organisation's collection.