Open Access

# $*$-wildness of some classes of $C^*$-algebras

### Abstract

We consider the complexity of the representation theory of free products of $C^*$-algebras. Necessary and sufficient conditions for the free product of finite-dimensional $C^*$-algebras to be $*$-wild is presented. As a corollary we get criteria for $*$-wildness of free products of finite groups. It is proved that the free product of a non-commutative nuclear $C^*$-algebra and the algebra of continuous functions on the one-dimensional sphere is $*$-wild. This result is applied to estimate the complexity of the representation theory of certain $C^*$-algebras generated by isometries and partial isometries.

Key words: ∗-Representations, free product, ∗-wild algebra.

### Article Information

 Title $*$-wildness of some classes of $C^*$-algebras Source Methods Funct. Anal. Topology, Vol. 12 (2006), no. 4, 315-325 MathSciNet MR2279869 Copyright The Author(s) 2006 (CC BY-SA)

### Authors Information

Sergio Albeverio
Institut fur Angewandte Mathematik, Universitat Bonn, Wegelerstr. 6, D--53115, Bonn, Germany; SFB 611, Bonn, Germany; BiBoS, Bielefeld, Germany; IZKS; CERFIM, Locarno, Switzerland; Accademia di Architettura, Mendrisio, Switzerland

Kate Jushenko
Department of Mathematics, Chalmers University of Technology, SE-41296, Goteborg, Sweden

Daniil Proskurin
Department of Cybernetics, Kyiv Taras Shevchenko National University, 64 Volodymyr\-s'ka, Kyiv, 01033, Ukraine

Yurii Samoilenko
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

### Citation Example

Sergio Albeverio, Kate Jushenko, Daniil Proskurin, and Yurii Samoilenko, $*$-wildness of some classes of $C^*$-algebras, Methods Funct. Anal. Topology 12 (2006), no. 4, 315-325.

### BibTex

@article {MFAT386,
AUTHOR = {Albeverio, Sergio and Jushenko, Kate and Proskurin, Daniil and Samoilenko, Yurii},
TITLE = {$*$-wildness of some classes of $C^*$-algebras},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {12},
YEAR = {2006},
NUMBER = {4},
PAGES = {315-325},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=386},
}