Representations of Higman-Thompson groups from Cuntz algebras

Autor:	Araújo, Francisco, Pinto, Paulo R.
Rok vydání:	2020
Předmět:	Mathematics - Operator Algebras Mathematics - Group Theory
Druh dokumentu:	Working Paper
Popis:	Every representation of the Cuntz algebra $\mathcal{O}_n$ leads to a unitary representation of the Higman-Thompson group $V_n$. We consider the family $\{\pi_x\}_{x\in [0,1[}$ of permutative representations of $\mathcal{O}_n$ that arise from the interval map $f(x)=nx$ (mod 1) acting on the Hilbert space that underlies each orbit, and then study the unitary equivalence and the irreducibility of the corresponding family $\{\rho_x\}_{x\in [0,1[}$ of representations of Higman-Thompson group $V_n$, showing that that these representations are indeed irreducible and moreover $\rho_x$ and $\rho_y$ are equivalent if and only if the orbits of $x$ and $y$ coincide. Comment: Introduction expanded
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2011.13679 Zobrazit plný text záznamu View this record from Arxiv