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

Authors

  • E. Jushenko 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
  • S. Albeverio Department of Mathematics, Chalmers University of Technology, SE-41296, Goteborg, Sweden
  • D. P. Proskurin Department of Cybernetics, Kyiv Taras Shevchenko National University, 64 Volodymyr\-s'ka, Kyiv, 01033, Ukraine
  • Yu. S. Samoilenko Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine 

DOI:

Keywords:

∗-Representations, free product, ∗-wild algebra

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.

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Published

2006-12-25

Issue

Vol. 12 No. 4 (2006)

Section

Articles

How to Cite

Jushenko, E., et al. “$*$-Wildness of Some Classes of $C^*$-Algebras”. Methods of Functional Analysis and Topology, vol. 12, no. 4, Dec. 2006, pp. 315-2, https://zen.imath.kiev.ua/index.php/mfat/article/view/325.