Crossed products of Toeplitz algebras and the $N$-adic rationals
Volume 148 / 2017
Colloquium Mathematicum 148 (2017), 39-45
MSC: Primary 46L35; Secondary 46L55.
DOI: 10.4064/cm6569-11-2016
Published online: 9 February 2017
Abstract
Let $G$ be a discrete group and $G_{+}$ be a generating subsemigroup with identity. If $\chi $ is a one-dimensional character of $G$, then it induces an automorphism on $C_{r}^{*}(G)$ and on the Toeplitz algebra $T_{G_{+}}$ associated to $(G,G_{+})$. When $(G,G_{+})$ is the naturally ordered group of $N$-adic rationals, we find complete isomorphism invariants of $T_{G_{+}}\rtimes _{\alpha _{\chi }}\mathbb {Z}$.
