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.

中文翻译：

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与一元群相关的代数中的无界推导

给定一个无限的、紧致的、一元的群$G$我们研究交叉积中无界推导的分解和结构$\文本{C}^{\ast }$-代数$C(G)\rtimes \mathbb{Z}$从翻译中获得$G$由密集循环子群的生成器。我们还研究了叉积的 Toeplitz 扩展中的推导，以及是否可以将无界推导从一个代数提升到另一个代数的问题。