Skip to main content
placeholder image

Homotopy of product systems and K-theory of Cuntz-Nica-Pimsner algebras

Journal Article


Abstract


  • We introduce the notion of a homotopy of product systems, and show that the

    Cuntz-Nica-Pimsner algebras of homotopic product systems over N^k have

    isomorphic K-theory. As an application, we give a new proof that the K-theory

    of a 2-graph C*-algebra is independent of the factorisation rules, and we

    further show that the K-theory of any twisted k-graph C*-algebra is independent

    of the twisting 2-cocycle. We also explore applications to K-theory for the

    C*-algebras of single-vertex k-graphs, reducing the question of whether the

    $K$-theory is independent of the factorisation rules to a question about

    path-connectedness of the space of solutions to an equation of Yang-Baxter

    type.

Publication Date


  • 2019

Citation


  • Fletcher, J., Gillaspy, E., & Sims, A. (2019). Homotopy of product systems and K-theory of Cuntz-Nica-Pimsner algebras. Retrieved from http://arxiv.org/abs/1911.00959v1

Web Of Science Accession Number


Abstract


  • We introduce the notion of a homotopy of product systems, and show that the

    Cuntz-Nica-Pimsner algebras of homotopic product systems over N^k have

    isomorphic K-theory. As an application, we give a new proof that the K-theory

    of a 2-graph C*-algebra is independent of the factorisation rules, and we

    further show that the K-theory of any twisted k-graph C*-algebra is independent

    of the twisting 2-cocycle. We also explore applications to K-theory for the

    C*-algebras of single-vertex k-graphs, reducing the question of whether the

    $K$-theory is independent of the factorisation rules to a question about

    path-connectedness of the space of solutions to an equation of Yang-Baxter

    type.

Publication Date


  • 2019

Citation


  • Fletcher, J., Gillaspy, E., & Sims, A. (2019). Homotopy of product systems and K-theory of Cuntz-Nica-Pimsner algebras. Retrieved from http://arxiv.org/abs/1911.00959v1

Web Of Science Accession Number