On diagonal actions of free group on the Cantor set
Korchagin, Anton
Original · EN
We study diagonal actions φ:F₂₂× K on the Cantor set which are given by φₐ=∂ₐ×α,φb=∂b×β. Under some restrictions on α,β we compute K*(C(₂× K)ᵣF₂). As an application in the case of α is Denjoy homeomorphism of the Cantor set and β=id we will show that C(₂× K)ᵣF₂ is Kirchberg algebra with K*(C(₂× K)ᵣF₂)=(Z∞,Z∞). Also we will check that C*-crossed product by Denjoy homeomorphism on the Cantor set is C*-algebra generated by weighted shift, namely C(K) C*(Tₓ) where x∈ {1,2}ᶻ is two-sided Fibonacci sequence.
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