C^*-algebras associated with the fundamental groups of graphs of groups

• Autores: R. Okayasu
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 97, Nº 1, 2005, págs. 49-72
• Idioma: inglés
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• Resumen

  • We construct a nuclear C∗-algebra associated with the fundamental group of a graph of groups of finite type. It is well-known that every word-hyperbolic group with zero-dimensional boundary, in other words, every group acting trees with finite stabilizers is given by the fundamental group of such a graph of groups. We show that our C∗-algebra is ∗-isomorphic to the crossed product arising from the associated boundary action and is also given by a Cuntz-Pimsner algebra. We also compute the K-groups and determine the ideal structures of our C∗-algebras.