The group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra

2019/03/12 by Izumi, Masaki, Sogabe, Taro
#46L80 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1903.04809

Abstract

We determine the group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra O_n+1 for finite n in terms of K-theory. We show that there is an example of a space for which the homotopy set is a non-commutative group, and hence the classifying space of the automorphism group of the Cuntz algebra for finite n is not an H-space. We also make an improvement of Dadarlat's classification of continuous fields of the Cuntz algebras in terms of vector bundles.

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• Classification of homomorphisms from C₀(0,1] to a C*-algebra