Year: 2025
Type: preprint
Abstract: Given a regular $\mathrm{C}^{*}$-algebraic locally compact quantum group $(S_r,Δ)$ with universal quantum group $(S_f,Δ_f)$, a $\mathrm{C}^{*}$-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 $\mathrm{C}^{*}$-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.
Source: arXiv (Cornell University)
Author: Gillespie, Matthew
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416540996
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