Geodesic
C$^{\ast }$-simplicity has no local obstruction
Forum of Mathematics, Sigma, Tome 10 (2022)

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In 2016, I solved a problem of de la Harpe from 2006: Is there a nondiscrete C$^{\ast }$-simple group? However the solution was not fully satisfactory, as the C$^{\ast }$-simple groups provided (and their operator algebras) are very close to discrete groups. All previously known examples are of this form. In this article I give yet another construction of nondiscrete C$^{\ast }$-simple groups. The statement in the title then follows. This in particular gives the first examples of nonelementary C$^{\ast }$-simple groups (in Wesolek’s sense). 
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     title = {C$^{\ast }$-simplicity has no local obstruction},
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Yuhei Suzuki. C$^{\ast }$-simplicity has no local obstruction. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.5

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