DOI: 10.53846/goediss-9727

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Aperiodic dynamical inclusions of C*-algebras

Jonathan Taylor¹

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“…The author would ilke to thank his doctoral advisor Ralf Meyer for all the assistance and expertise he provided. This article consists of results from the author's PhD thesis [24].…”

Section: Introductionmentioning

confidence: 99%

Aperiodic dynamical inclusions of $C^*$-algebras

2023

Preprint

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We define the local multiplier module of a Hilbert module in analogy to the local multiplier algebra for C ˚-algebras. We use properties of the local multiplier module to lift non-closed actions on C ˚-algebras by Hilbert bimodules to closed actions on local multiplier algebras, and descend known results on such closed actions down to their unclosed counterparts. We define aperiodic dynamical inclusions and characterise them as crossed products by inverse semigroup actions. We describe the slice structure for such inclusions and show that all slices arise as linear combinations of slices already present in the inverse semigroup action.

“…The author would ilke to thank his doctoral advisor Ralf Meyer for all the assistance and expertise he provided. This article consists of results from the author's PhD thesis [24].…”

Section: Introductionmentioning

confidence: 99%

Aperiodic dynamical inclusions of $C^*$-algebras

2023

Preprint

View full text Add to dashboard Cite

We define the local multiplier module of a Hilbert module in analogy to the local multiplier algebra for C ˚-algebras. We use properties of the local multiplier module to lift non-closed actions on C ˚-algebras by Hilbert bimodules to closed actions on local multiplier algebras, and descend known results on such closed actions down to their unclosed counterparts. We define aperiodic dynamical inclusions and characterise them as crossed products by inverse semigroup actions. We describe the slice structure for such inclusions and show that all slices arise as linear combinations of slices already present in the inverse semigroup action.

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