UNBOUNDED DERIVATIONS IN ALGEBRAS ASSOCIATED WITH MONOTHETIC GROUPS

Given an infinite, compact, monothetic group $G$ we study decompositions and structure of unbounded derivations in a crossed product $\text{C}^{\ast }$ -algebra $C(G)\rtimes \mathbb{Z}$ 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.