# Unbounded Derivations in Algebras Associated with Monothetic Groups

## TL;DR

This paper investigates the structure and properties of unbounded derivations in certain crossed product C*-algebras associated with infinite monothetic groups, including their decompositions, extensions, and liftings.

## Contribution

It provides new insights into the structure of unbounded derivations in crossed products and Toeplitz extensions related to monothetic groups, including lifting properties.

## Key findings

- Characterization of unbounded derivations in $C(G)\rtimes\Z$
- Analysis of derivations in Toeplitz extensions
- Results on lifting unbounded derivations between algebras

## Abstract

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