Geodesic
Unitary groups, $\boldsymbol{K}$-theory, and traces
Glasgow mathematical journal, Tome 66 (2024) no. 2, pp. 229-251

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DOI

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).
DOI : 10.1017/S0017089523000447
Mots-clés : K-theory, traces, unitary groups, C*-algebras 
Sarkowicz, Pawel. Unitary groups, $\boldsymbol{K}$-theory, and traces. Glasgow mathematical journal, Tome 66 (2024) no. 2, pp. 229-251. doi: 10.1017/S0017089523000447
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     title = {Unitary groups, $\boldsymbol{K}$-theory, and traces},
     journal = {Glasgow mathematical journal},
     pages = {229--251},
     year = {2024},
     volume = {66},
     number = {2},
     doi = {10.1017/S0017089523000447},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089523000447/}
}
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