Group Actions Seminar: Armstrong, Li (Update)

See the updated schedule for the group actions seminar below. Note that the order of the
talks has changed from what was originally posted. The seminar will be on Monday 10 July 
at the University of Sydney. The schedule, titles and abstracts are below.  

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Noon - 1pm, Carslaw 375 


Speaker: Becky Armstrong, The University of Sydney 

Title: Group actions, groupoids, and their C*-algebras 

Abstract: C*-algebras were first introduced in order to model physical observables
in quantum mechanics, but are now studied more abstractly in pure mathematics.  Much of
the current research of C*-algebraists involves constructing interesting classes of
C*-algebras from various mathematical objects---such as groups, groupoids, and
directed graphs---and studying their properties.  Groupoid C*-algebras were
introduced by Renault in 1980, and provide a unifying model for C*-algebras associated
to groups, group actions, and graphs.  In this talk, I will define topological groupoids
and examine Renault’s construction of groupoid C*-algebras.  I will discuss several
examples of groupoids, including group actions and graph groupoids, and will conclude
with a brief description of my PhD research.

1-3pm Lunch 

3-4pm, Carslaw 375 

Speaker: Huanhuan Li, Western Sydney University 

Title: Graded Steinberg algebras and their representations 

Joint work with Pere Ara, Roozbeh Hazrat and Aidan Sims.

Abstract: We study the category of left until graded modules over the Steinberg algebra
of a graded ample Hausdorff groupoid.  In the first part of the paper, we show that this
category is isomorphic to the category of unital left modules over the Steinberg algebra
of the skew-product groupoid arising from the grading.  To do this, we show that the
Steinberg algebra of the skew product is graded isomorphic to a natural generalisation
of the the Cohen-Montgomery smash product of the Steinberg algebra of the underlying
groupoid with the grading group.  In the second part of the paper, we study the minimal
(that is, irreducible) representations in the category of graded modules of a Steinberg
algebra, and establish a connection between the annihilator ideals of these minimal
representations, and effectiveness of the groupoid.  

Specialising our results, we produce a representation of the monoid of graded finitely 
generated projective modules over a Leavitt path algebra.  We deduce that the lattice of 
order-ideals in the K_0-group of the Leavitt path algebra is isomorphic to the 
lattice of graded ideals of the algebra.  We also investigate the graded monoid for 
Kumjian–Pask algebras of row-finite k-graphs with no sources.  We prove that these 
algebras are graded von Neumann regular rings, and record some structural consequences 
of this.