Homotopy of Product Systems and K-Theory of Cuntz-Nica-Pimsner Algebras

James Fletcher, Elizabeth Gillaspy, Aidan Sims

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce the notion of a homotopy of product systems, and show that the Cuntz-Nica-Pimsner algebras of homotopic product systems over Nk 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 2-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.

Original languageEnglish
Pages (from-to)307-338
Number of pages32
JournalIndiana University Mathematics Journal
Volume71
Issue number5
DOIs
StatePublished - 2022

Keywords

  • Cuntz-Nica-Pimsner
  • higher-rank graph
  • K-theory
  • Product system

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