## The $C^\ast$-algebra of an affine map on the 3-torus

### Summary

Summary: We study the $C^*$-algebra of an affine map on a compact abelian group and give necessary and sufficient conditions for strong transitivity when the group is a torus. The structure of the $C^*$-algebra is completely determined for all strongly transitive affine maps on a torus of dimension one, two or three.

46L35, 37B99