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arXiv · 2305.15989

Unitary groups, K-theory and traces

Pawel Sarkowicz
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Abstract

We show that continuous group homomorphisms between unitary groups of unital C*-algebras induce maps between spaces of continuous real-valued affine functions on the trace simplices. Under certain $K$-theoretic regularity conditions, these maps can be seen to commute with the pairing between $K_0$ and traces. If the homomorphism is contractive and sends the unit circle to the unit circle, the map between spaces of continuous real-valued affine functions can further be shown to be unital and positive (up to a minus sign).

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Pawel Sarkowicz. 2023-05-25. Unitary groups, K-theory and traces. https://arxiv.org/abs/2305.15989

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