MAXIMAL IDEALS OF REDUCED GROUP C*-ALGEBRAS AND THOMPSON’S GROUPS

Brix KA, Bruce C, Li K, Scarparo E (2026)

Publication Type: Journal article

Publication year: 2026

Journal

Transactions of the American Mathematical Society American Mathematical Society

Book Volume: 379

Pages Range: 4307-4321

Journal Issue: 6

DOI: 10.1090/tran/9627

Abstract

Given a conditional expectation P from a C*-algebra B onto a C*-subalgebra A, we observe that induction of ideals via P, together with a map which we call co-induction, forms a Galois connection between the lattices of ideals of A and B. Using properties of this Galois connection, we show that, given a discrete group G and a stabilizer subgroup Gx for the action of G on its Furstenberg boundary, induction gives a bijection between the set of maximal co-induced ideals of C^∗(Gx) and the set of maximal ideals of Cr^∗(G). As an application, we prove that the reduced C*-algebra of Thompson’s group T has a unique maximal ideal. Furthermore, we show that, if Thompson’s group F is amenable, then Cr^∗(T) has infinitely many ideals.

Authors with CRIS profile

Kang Li Juniorprofessur für Mathematik (Darstellungstheorie und Operatoralgebren)

Involved external institutions

Lund University / Lunds universitet

Sweden (SE) Newcastle University

United Kingdom (GB) Federal University of Pelotas / Universidade Federal de Pelotas (UFPEL)

Brazil (BR)

How to cite

APA:

Brix, K.A., Bruce, C., Li, K., & Scarparo, E. (2026). MAXIMAL IDEALS OF REDUCED GROUP C*-ALGEBRAS AND THOMPSON’S GROUPS. Transactions of the American Mathematical Society, 379(6), 4307-4321. https://doi.org/10.1090/tran/9627

MLA:

Brix, Kevin Aguyar, et al. "MAXIMAL IDEALS OF REDUCED GROUP C*-ALGEBRAS AND THOMPSON’S GROUPS." Transactions of the American Mathematical Society 379.6 (2026): 4307-4321.

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