Clone automorphisms and hypersubstitutions

K. Denecke, K. Głazek, St. Niwczyk

A hypersubstitution maps the operation symbols of a type $\tau$ to terms of the same arity and can be uniquely extended to a mapping defined on the set of all terms of this type. In this paper we prove that the group of all clone automorphisms of an algebra $\mathcal A$ is isomorphic to a certain group of hypersubstitutions supposed the variety $V(\mathcal A)$ generated by $\mathcal A$ is solid.