Characterizing group C*-algebras through their unitary groups: the Abelian case
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Títol
Characterizing group C*-algebras through their unitary groups: the Abelian caseData de publicació
2010-07Editor
Walter de GruyterISSN
0933-7741Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
https://www.degruyter.com/view/journals/form/22/4/article-p811.xmlVersió
info:eu-repo/semantics/submittedVersionParaules clau / Matèries
Resum
We study to what extent group C*-algebras are characterized by their unitary groups. A complete characterization of which Abelian group C*-algebras have isomorphic unitary groups is obtained. We compare these results ... [+]
We study to what extent group C*-algebras are characterized by their unitary groups. A complete characterization of which Abelian group C*-algebras have isomorphic unitary groups is obtained. We compare these results with other unitary-related invariants of C*(Γ), such as the K-theoretic K1(C*(Γ)) and find that C*-algebras of nonisomorphic torsion-free Abelian groups may have isomorphic K1-groups, in sharp contrast with the well-known fact that C*(Γ) (even Γ) is characterized by the topological group structure of its unitary group when Γ is torsion-free and Abelian [-]
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Forum Mathematicum, vol. 22, no. 4 (Jul. 2010), pp 811–824Drets d'accés
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