2011/12/29 by Alex Kumjian, Kumjian, Alex, David Pask +3 · 2 citations
Mathematics · Physics and Astronomy · #55N10 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Primary 46L05 #Secondary 18G60
paper · pdf · doi:10.48550/arxiv.1112.6233
openalex publication_date 2011/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define the categorical cohomology of a k-graph Λ and show that the first three terms in this cohomology are isomorphic to the corresponding terms in the cohomology defined in our previous paper. This leads to an alternative characterisation of the twisted k-graph C*-algebras introduced there. We prove a gauge-invariant uniqueness theorem and use it to show that every twisted k-graph C*-algebra is isomorphic to a twisted groupoid C*-algebra. We deduce criteria for simplicity, prove a Cuntz-Krieger uniqueness theorem and establish that all twisted k-graph C*-algebras are nuclear and belong to the bootstrap class.