The 𝐶*-algebra of the exponential function

Thomsen, Klaus

doi:10.1090/S0002-9939-2013-11716-8

The $C^*$-algebra of the exponential function
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Proc. Amer. Math. Soc. 142 (2014), 181-189 Request permission

Abstract:

The complex exponential function $e^z$ is a local homeomorphism and therefore gives rise to an étale groupoid and a $C^*$-algebra. We show that this $C^*$-algebra is simple, purely infinite, stable and classifiable by K-theory, and has both K-theory groups isomorphic to $\mathbb Z$. The same methods show that the $C^*$-algebra of the anti-holomorphic function $\overline {e^z}$ is the stabilisation of the Cuntz-algebra $\mathcal O_3$.

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