The Ladder Technique -- Quantum Groups

2025/04/16 by Matthew Gillespie, Gillespie, Matthew
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Quantum many-body systems #math.OA

paper · pdf · doi:10.48550/arxiv.2504.11677

openalex publication_date 2025/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a regular C^*-algebraic locally compact quantum group (S_r,Δ) with universal quantum group (S_f,Δ_f), a C^*-algebra A, and a sufficiently well-behaved full coaction S_f \oversetα\curvearrowright A, we construct natural lattice isomorphisms from the strongly coaction invariant ideals of A to the strongly coaction invariant ideals of full and reduced crossed product C^*-algebras as an application of the `ladder technique' developed by the author, S. Kaliszewski, John Quigg and Dana P. Williams. In particular, these lattice isomorphisms are determined by either the maximality or normality of the coaction α. This result directly generalizes a recent theorem proven by the aforementioned authors for locally compact groups, which in turn generalized a theorem of Elliot Gootman and Aldo Lazar for amenable groups.

Related

• Bijections Between Sets of Invariant Ideals, Via the Ladder Technique
• Symmetries of a generic coaction
• Induced coactions along a homomorphism of locally compact quantum groups
• Mapping ideals of quantum group multipliers
• Fundamental isomorphism theorems for quantum groups