• Corpus ID: 117764570

Twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs

@article{Whitehead2013TwistedRC,
  title={Twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs},
  author={Benjamin Whitehead},
  journal={arXiv: Operator Algebras},
  year={2013}
}

• Benjamin Whitehead
• Published 25 October 2013
• Mathematics
• arXiv: Operator Algebras

To each finitely aligned higher-rank graph $\Lambda$ and each $\mathbb{T}$-valued 2-cocycle on $\Lambda$, we associate a family of twisted relative Cuntz-Krieger algebras. We show that each of these algebras carries a gauge action, and prove a gauge-invariant uniqueness theorem. We describe an isomorphism between the fixed point algebras for the gauge actions on the twisted and untwisted relative Cuntz-Krieger algebras. We show that the quotient of a twisted relative Cuntz-Krieger algebra by a gauge-invariant ideal is canonically isomorphic to a twisted relative Cuntz-Krieger algebra associated to a subgraph. We use this to provide a complete graph-theoretic description of the gauge-invariant ideal structure of each twisted relative Cuntz-Krieger algebra.