Free nilpotent groups are $C^*$-superrigid
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Abstract:
The free nilpotent group $G_{m,n}$ of class $m$ and rank $n$ is the free object on $n$ generators in the category of nilpotent groups of class at most $m$. We show that $G_{m,n}$ can be recovered from its reduced group $C^*$-algebra, in the sense that if $H$ is any group such that $C^*_r(H)$ is isomorphic to $C^*_r(G_{m,n})$, then $H$ must be isomorphic to $G_{m,n}$.References
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Additional Information
- Tron Omland
- Affiliation: Department of Mathematics, University of Oslo, NO-0316 Oslo, Norway; Department of Computer Science, Oslo Metropolitan University, NO-0130 Oslo, Norway
- MR Author ID: 930118
- Email: trono@math.uio.no
- Received by editor(s): November 2, 2018
- Received by editor(s) in revised form: April 19, 2019
- Published electronically: July 9, 2019
- Additional Notes: The author was funded by the Research Council of Norway through FRINATEK, project no. 240913.
- Communicated by: Adrian Ioana
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 283-287
- MSC (2010): Primary 46L05, 20F18
- DOI: https://doi.org/10.1090/proc/14678
- MathSciNet review: 4042850