Year: 2018
Type: preprint
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 $G_{m,n}$.
Source: arXiv (Cornell University)
Author: Omland, Tron
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Norges Forskningsråd
Award: G1338491623
OpenAlex ID: W2794707194