Lifting Commutation Relations in Cuntz Algebras

2015/01/13 by Blackadar, Bruce
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1501.03183

Abstract

We examine splitting of the quotient map from the full free product A*B, or the unital free product A*_{\mathbb C}B, to the (maximal) tensor product A⊗ B, for unital C*-algebras A and B. Such a splitting is very rare, but we show there is one if A and B are both the Cuntz algebra O₂ or O_∞, and in a few other cases. The splitting is not explicit (and in principle probably cannot be). We also describe severe K-theoretic obstructions to a splitting.

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