Representations of Higman-Thompson groups from Cuntz algebras

2020/11/27 by Francisco Araújo, Araújo, Francisco, Paulo R. Pinto +1
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2011.13679

openalex publication_date 2020/11/27 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Every representation of the Cuntz algebra O_n leads to a unitary representation of the Higman-Thompson group V_n. We consider the family \π_x\_{x∈ [0,1[} of permutative representations of 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 \ρ_x\_{x∈ [0,1[} of representations of Higman-Thompson group V_n, showing that that these representations are indeed irreducible and moreover ρ_x and ρ_y are equivalent if and only if the orbits of x and y coincide.

Related

• Atomic representations of R. Thompson's groups and Cuntz's algebra
• Full groups of Cuntz-Krieger algebras and Higman-Thompson groups
• Endomorphisms of the Cuntz Algebras and the Thompson Groups
• Representations of Cuntz algebras, loop groups and wavelets
• Generalized permutative representations of Cuntz algebras