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${}^{\ast }$-algebra $C(G)⋊\mathbb{Z}$ 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.

References in corpus (1)

• The Quantum Pair of Pants