2020/10/02 by Taro, Sogabe
#FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2010.00750
We investigate an invariant for continuous fields of the Cuntz algebra On+1 introduced in our previous work, and find a way to obtain a continuous field of \mathbbMn(O_∞) from that of On+1 using the construction of the invariant. By Brown's representability theorem, this gives a bijection from the set of the isomorphism classes of continuous fields of On+1 to those of \mathbbMn(O_∞). As a consequence, we obtain a new proof for M. Dadarlat's classification result of continuous fields of On+1 arising from vector bundles, which corresponds to those of \mathbbMn(O_∞) stably isomorphic to the trivial field.