English

On reduced twisted group C*-algebras that are simple and/or have a unique trace

Operator Algebras 2017-06-06 v5 Group Theory

Abstract

We study the problem of determining when the reduced twisted group C*-algebra associated with a discrete group G is simple and/or has a unique tracial state, and present new sufficient conditions for this to hold. One of our main tools is a combinatorial property, that we call the relative Kleppner condition, which ensures that a quotient group G/H acts by freely acting automorphisms on the twisted group von Neumann algebra associated to a normal subgroup H. We apply our results to different types of groups, e.g. wreath products and Baumslag-Solitar groups.

Keywords

Cite

@article{arxiv.1606.02637,
  title  = {On reduced twisted group C*-algebras that are simple and/or have a unique trace},
  author = {Erik Bédos and Tron Omland},
  journal= {arXiv preprint arXiv:1606.02637},
  year   = {2017}
}

Comments

37 pages. Section 4 has been slightly reorganized and improved, and one example has been added to Section 5. A few redactional changes and some typos corrected throughout the text. Final version, to appear in J. Noncommut. Geom