Type: Seminar

Modified: Mon 5 Jun 2017 1040

Distribution: World

Expiry: 10 Jul 2017

CalTitle1: Armstrong, Group actions, groupoids, and their C*-algebras

Calendar2: 10 Jul 2017 1500-1600

CalLoc2: Carslaw 375

CalTitle2: Li, Graded Steinberg algebras and their representations

Auth: timothyb@como.maths.usyd.edu.au

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. -------------------------------------------------------------------------- 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 Kumjianâ€“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.

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