Remarks on C-discrete inclusions

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. Furthermore, we...

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Bibliographic Details
Published in:arXiv.org 2024-09
Main Authors: Roberto Hernández Palomares, Nelson, Brent
Format: Article
Language:English
Subjects:
Algebra
Inclusions
Set theory
Tensors
Online Access:Get full text
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Summary: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. Furthermore, 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. Finally, we define ``freeness'' for actions of tensor categories on C*-algebras, and show simplicity is preserved under taking reduced crossed products.
ISSN:2331-8422