2013/10/25 by Benjamin Whitehead, Whitehead, Benjamin
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1310.7045
openalex publication_date 2013/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To each finitely aligned higher-rank graph Λ and each \mathbbT-valued 2-cocycle on Λ, 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.