Geometry of a crossed product

Nikolaev, Igor

doi:10.1090/S0002-9939-99-05253-3

Geometry of a crossed product
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by Igor Nikolaev PDF

Proc. Amer. Math. Soc. 128 (2000), 1177-1183 Request permission

Abstract:

We introduce a continuous dimension function $\alpha : \bullet \to \mathbb {R}$ on the Grothendieck group $K_0$ over the crossed product $C^*$-algebra $C(X)\rtimes _{\phi }\mathbb {Z}$. The function $\alpha$ has an elegant geometry: on every minimal flow $\phi ^t$ it takes the value of the “rotation number" of $\phi ^t$; such a problem was posed in 1936 by A. Weil.

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