2018
Том 70
№ 8

# On the Group $C^{*}$-Algebras of a Semidirect Product of Commutative and Finite Groups

Abstract

By using representations of general position and their properties, we give the description of group $C^{*}$-algebras for semidirect products $\mathbb{Z}^d \times G_f$, where $G_f$ is a finite group, in terms of algebras of continuous matrix-functions defined on some compact set with boundary conditions. We present examples of the $C^{*}$-algebras of affine Coxeter groups.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 5, pp 826-836.

Citation Example: Samoilenko Yu. S., Yushchenko K. Yu. On the Group $C^{*}$-Algebras of a Semidirect Product of Commutative and Finite Groups // Ukr. Mat. Zh. - 2005. - 57, № 5. - pp. 697–705.

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