Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, June 12, 2018.

     .
events for the
events containing  

(Requires a password.)
More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
       May 2018              June 2018              July 2018      
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
        1  2  3  4  5                   1  2    1  2  3  4  5  6  7
  6  7  8  9 10 11 12    3  4  5  6  7  8  9    8  9 10 11 12 13 14
 13 14 15 16 17 18 19   10 11 12 13 14 15 16   15 16 17 18 19 20 21
 20 21 22 23 24 25 26   17 18 19 20 21 22 23   22 23 24 25 26 27 28
 27 28 29 30 31         24 25 26 27 28 29 30   29 30 31            
                                                                   

Tuesday, June 12, 2018

1:00 pm in 341 Altgeld Hall,Tuesday, June 12, 2018

Representations of Toeplitz-Cuntz-Krieger algebras

Adam Dor-On (Technion)

Abstract: By a result of Glimm, we know that classifying representations of non-type-I $C^*$-algebras up to unitary equivalence is essentially impossible (at least with countable structures). Instead of this, one either restricts to a tractable subclass or weakens the invariant. In the theory of free semigroup algebras, this is done for Toeplitz-Cuntz algebras, and is achieved via two key results in the theory: the first is a theorem of Davidson, Katsoulis and Pitts on the $2\times 2$ structure of free semigroup algebras, and the second is a Lebesgue-von Neumann-Wold decomposition theorem of Kennedy. This talk is about joint work with Ken Davidson and Boyu Li, where we generalize this theory to representations of Toeplitz-Cuntz-$Krieger$ algebras associated to a directed graph $G$. We prove a structure theorem akin to that of Davidson, Katsoulis and Pitts, and provide a Lebesuge-von Neumann Wold decomposition using Kennedy's theorem. We discuss some of the difficulties and similarities when passing to the more general context of operator algebras associated to directed graphs.