All extensions of \(C^*_r(\mathbb F_n)\) are semi-invertible

DOI10.1007/S00208-008-0232-5zbMath1151.46040OpenAlexW2063718222MaRDI QIDQ943353

Klaus Thomsen

Publication date: 9 September 2008

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-008-0232-5

zbMATH Keywords

free groupCalkin algebrasplit extensionasymptotically splitreduced group \(C^*\)-algebrasemi-invertiblestrongly homotopic

Mathematics Subject Classification ID

(C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) General theory of (C^*)-algebras (46L05) Ext and (K)-homology (19K33) Tensor products of (C^*)-algebras (46L06)

Related Items (2)

Semi-invertible extensions of \(C^{*}\)-algebras ⋮ Extensions of the reduced group \(C^{*}\)-algebra of a free product of amenable groups

Cites Work

• Extensions of \(C^*\)-algebras and \(K\)-homology
• The Connes-Higson construction is an isomorphism
• A new application of random matrices: \(\operatorname{Ext} (C_{\text{red}}^*(F_2))\) is not a group
• Asymptotic representations of the reduced C*-algebra of a free group: an example
• $E$-Theory is a Special Case of $KK$-Theory
• K-theoretic amenability for discrete groups.
• On the Lack of Inverses to C*-Extensions Related to Property T Groups
• A \(C^*\)-algebra \(\mathcal A\) for which Ext (\(\mathcal A\)) is not a group
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