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On C*-algebras related to constrained representations of a free group

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Abstract

We consider representations of the free group F 2 on two generators for which the norm of the sum of the generators and their inverses is bounded by some number µ ∈ [0, 4]. These µ-constrained representations determine a C*-algebra A µ for each µ ∈ [0, 4]. If µ = 4, this gives the full group C*-algebra of F 2. We prove that these C*-algebras form a continuous bundle of C*-algebras over [0, 4] and evaluate their K-groups.

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    V. M. Manuilov

  2. Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technology, Harbin, 150001, P. R. China

    V. M. Manuilov

  3. Department of Mathematics and Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technology, Harbin, 150001, P. R. China

    Chao You

Authors
  1. V. M. Manuilov
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  2. Chao You
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Correspondence to V. M. Manuilov.

Additional information

The first-named author acknowledges a partial support by RFBR (grant no. 08-01-00034). The second-named author was partially supported by National Natural Science Foundation of China (no. 10971150) and State Scholarship Fund of China (no. 2008612056).

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Manuilov, V.M., You, C. On C*-algebras related to constrained representations of a free group. Russ. J. Math. Phys. 17, 280–287 (2010). https://doi.org/10.1134/S1061920810030039

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  • DOI: https://doi.org/10.1134/S1061920810030039

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