Sam Walters - K-theory of non commutative spheres arising from the Fourier automorphism

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Sam Walters - K-theory of non commutative spheres arising from the Fourier automorphism

SAM WALTERS, Department of Mathematics and Computer Science, University of Northern British Columbia, Prince George, British Columbia V2K 4A2, Canada

K-theory of non commutative spheres arising from the Fourier automorphism

It is shown that for a dense $G_\delta$ set of the real number $\theta$ (containing the rationals) there is an isomorphism $K_0(A_\theta\rtimes_\sigma\Bbb Z_4)\cong\Bbb Z^9$ , where $A_\theta$ is the rotation $C^\ast$ -algebra generated by unitaries U,V satisfying $VU=e^{2\pi i\theta}UV$ and $\sigma$ is the Fourier automorphism given by $\sigma(U)=V$ , $\sigma(V)=U^{-1}$ . More precisely, a basis consisting of nine canonical modules is explicitly given. It is also shown that for a dense $G_\delta$ one has $K_1(A_\theta\rtimes_\sigma\Bbb Z_4)=0$ .