Wednesday, March 24, 2021
10:00 a.m. (sharp)
PhD Candidate: Mihai Alboiu
Supervisor: George Elliott
Thesis title: The Stable Rank of Diagonal Ash Algebras
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Building on the work of Lutley, we study a certain subclass of recursive subhomogeneous algebras, called DSH algebras, in which the pullback maps are all diagonal in a suitable sense. We examine inductive limits of DSH algebras, where each bonding map is itself diagonal in an appropriate way, and show that every simple algebra thus obtained has stable rank one. We are therefore able to show that every simple dynamical crossed product has stable rank one and that the Toms-Winter Conjecture holds for such algebras.
We also introduce the class of non-unital DSH algebras and make partial progress towards showing that inductive limits of such algebras with diagonal maps have stable rank one. Moreover, we investigate more intrinsic notions of a diagonal map and matrix unit compatibility and show that in the full matrix algebra setting they agree with their usual (global) counterparts.
A copy of the thesis can be found here: ALBOIU_Thesis_Draft_Updated
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