Aperiodic dynamical inclusions of C*-algebras

by Jonathan Peter Taylor
Doctoral thesis
Date of Examination:2022-09-22
Date of issue:2023-02-16
Advisor:Ralf Meyer
Referee:Thomas Schick
Referee:Chenchang Zhu
Persistent Address: http://dx.doi.org/10.53846/goediss-9727

 

 

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Abstract

English

We define an analogue of the local multiplier algebra for Hilbert modules and use properties of this localisation to enrich non-closed actions on C*-algebras to closed actions on local multiplier algebras. This is used to 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 show that in the commutative case we show that weak Cartan subalgebras are maximal abelian, and show such inclusions have twisted groupoid models.
Keywords: operator algebras; C*-algebras; crossed product; inverse semigroup; étale groupoid
 
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