Nonseparable CCR algebras

2021/04/16 by Ilijas Farah, Farah, Ilijas, Najla Manhal +1
Mathematics · #57M25 #57M27 #FOS: Mathematics #Logic (math.LO) #Operator Algebras (math.OA) #math.LO #math.OA #msc:57M25 #msc:57M27

paper · pdf · doi:10.48550/arxiv.2104.08240

Minor changes (other than the new documentstyle). To appear in International Journal of Mathematics

arxiv created 2021/08/11 · arxiv updated 2021/08/12

Abstract

Extending a result of the first author and Katsura, we prove that for every UHF algebra A of infinite type, in every uncountable cardinality κ there are 2^κ nonisomorphic approximately matricial C*-algebras with the same K₀ group as A. These algebras are group \cstar-algebras `twisted' by prescribed canonical commutation relations (CCR), and they can also be considered as nonseparable generalizations of noncommutative tori.

Related

• An infinite family of non-isomorphic C*-algebras with identical K-theory
• Nonseparable UHF algebras II: Classification
• Strong Morita equivalence of higher-dimensional noncommutative tori. II
• Nonseparable UHF algebras I: Dixmier's problem
• The K-Theory of a Simple Separable Exact C*-Algebra Not Isomorphic to Its Opposite Algebra