Abstract
Let $\theta$ be an irrational number and $A_\theta$ be the corresponding irrational rotation $C^*$-algebra. For any $k\in N\cup\{\infty\}$ let $A_\theta^k$ be the dense $*$-subalgebra of $k$-times continuously differentiable elements in $A_\theta$ with respect to the canonical action of the two dimensional torus and let $A_\theta^0=A_\theta$. In the present paper we will show that there is an approximately inner $*$-derivation of $A_\theta^\infty$ to $A_\theta^\infty$ which is not inner if and only if $\theta$ is a non-generic irrational number.
Citation
Kazunori KODAKA. "Approximately Inner $*$-Derivations of Irrational Rotation $C^*$-Algebras." Tokyo J. Math. 13 (1) 207 - 219, June 1990. https://doi.org/10.3836/tjm/1270133015
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