Let $ A_\theta$ be an irrational rotation algebra and $B_\theta$ be the AF-algebra defined by Effros and Shen. Then we have monomorphisms of $A_\theta$ into $B_\theta$. In the present paper we will show that there are automorphisms of $A_\theta$ which can not be extended to any automorphism of $B_\theta$ for any monomorphism of $A_\theta$ into $ B_\theta$.
"On Automorphisms of Irrational Rotation Algebras." Tokyo J. Math. 12 (1) 91 - 97, June 1989. https://doi.org/10.3836/tjm/1270133550