On twisted higher-rank graph 𝐶*-algebras

Autor:	David Pask, Aidan Sims, Alex Kumjian
Rok vydání:	2015
Předmět:	Discrete mathematics Pure mathematics Uniqueness theorem for Poisson's equation Applied Mathematics General Mathematics MathematicsofComputing_GENERAL Equivariant cohomology Graph Cohomology Mathematics
Zdroj:	Transactions of the American Mathematical Society. 367:5177-5216
ISSN:	1088-6850 0002-9947
DOI:	10.1090/s0002-9947-2015-06209-6
Popis:	We define the categorical cohomology of a k k -graph Λ \Lambda 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 k -graph C ∗ C^* -algebras introduced there. We prove a gauge-invariant uniqueness theorem and use it to show that every twisted k k -graph C ∗ C^* -algebra is isomorphic to a twisted groupoid C ∗ C^* -algebra. We deduce criteria for simplicity, prove a Cuntz-Krieger uniqueness theorem and establish that all twisted k k -graph C ∗ C^* -algebras are nuclear and belong to the bootstrap class.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::05f144a28165c3046fa99f1079c2b545 https://doi.org/10.1090/s0002-9947-2015-06209-6 Zobrazit plný text záznamu