Unbounded Derivations in Algebras Associated with Monothetic Groups

Abstract

Given an infinite, compact, monothetic group G we study decompositions and structure of unbounded derivations in a crossed product C∗ -algebra C(G)⋊Z obtained from a translation on G by a generator of a dense cyclic subgroup. We also study derivations in a Toeplitz extension of the crossed product and the question whether unbounded derivations can be lifted from one algebra to the other.