2024/09/26 by Roberto Hernández Palomares, Palomares, Roberto Hernández, Brent Nelson +1 · 1 citation
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Operator Algebras (math.OA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2409.18161
openalex publication_date 2024/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We obtain a Galois correspondence between the lattice of intermediate C*-discrete subalgebras intermediate to a given irreducible C*-discrete inclusion, and characterize these as targets of compatible expectations under a traciality condition. Furthermore, we define freeness for actions of tensor categories on C*-algebras, and show simplicity is preserved under taking reduced crossed products. Finally, we show under certain constraints that A-valued semicircular systems give rise to C*-discrete inclusions, and thus are crossed products by an action of a tensor category. Along the way, we show the set of single algebraic generators of a dualizable bimodule forms an open subset.