DePaul Algebra Seminar


 

 

When:  Friday, October 10, at 3:30, Room: TBA


Speaker:  Gene Abrams, University of Colorado at Colorado Springs


Title:  Leavitt algebras and Leavitt path algebras

 

Abstract: Most of the rings one encounters as ``basic examples" have what's known as the Invariant Basis Number

property: for every pair of positive integers m and n, if the free left R-modules $_RR^{(m)}$ and $_RR^{(n)}$ are

isomorphic, then m=n. There are, however, many important classes of rings which do not have this property.

While at first glance such rings might seem pathological, in fact they arise quite naturally in a number of contexts

(e.g. as endomorphism rings of infinite dimensional vector spaces), and possess a significant (perhaps surprising)

amount of structure.

 

  In this presentation we describe a class of such rings, the (now-classical) Leavitt algebras, and then describe their

recently developed generalizations, the Leavitt path algebras.   One of the nice aspects of this subject is that

pictorial representations  (using graphs) of the algebras are readily available.

  In addition, there are strong connections between these algebraic structures and a class of C*-algebras

(the ``Cuntz-Krieger graph C*-algebras"), a connection which is currently the subject of great interest to both

algebraists and analysts.

 

 
 

 

Coffee/Cookies at 3:10 in SAC 545

 


Schedule for Academic Year 2008-2009:

(includes all algebra/combinatorics talks from the Math Department Colloquium Series)

Unless otherwise stated, Wednesdays at 3:30, with coffee/cookies at 3:10 in room SAC 545

 

Fall 2008:

 
September 17, 2008, at 3:30 P.M. in Room: Levan 403
Speaker: Ryan Kinser, University of Michigan
TitleRank functions on rooted tree quivers”
 
October 1, 2008, at 2:30 PM in Room SAC 545
Speaker: Kari Ragnarsson, DePaul University
Title: “Fusion systems and the double Burnside ring”
 
October 10, 2008 (Friday) at 3:30 P.M. in Room: TBA
Speaker: Gene Abrams, University of Colorado at Colorado Springs
Title“Leavitt algebras and Leavitt path algebras”
 
October 17, 2008 (Friday) at 3:30 P.M., Room TBA (Colloquium Talk)
Speaker: Ian Musson, University of Wisconsin-Milwaukee
Title: TBA
 
November 11, 2008 (Tuesday) at 3:30 P.M. in Room: TBA
Speaker: Kathryn Nyman, Loyola University of Chicago
TitleTBA
 
 
 

 


 

Summer 2008:

 
July 21, 2008 (Monday), at 3:00 P.M. in Room: SAC 546
Speaker:  Apoorva Khare, University of California-Riverside
Title"Classical and quantum infinitesimal Hecke algebras over sl_2"
 
August 5, 2008 (Tuesday), at 2:30, Room: SAC 546
Speaker: Akaki Tikaradze, University of Toledo
Title: “Representations of Infinitesimal Hecke algebras”
 

 


 

 

Schedule for Academic Year 2007-2008:

(includes all algebra/combinatorics talks from the Math Department Colloquium Series)

SPRING 2008


April 10, 2008 (Thursday), at 3:30 P.M. in Levan 305
Speaker: Yuri Bahturin, Moscow State University and Memorial Univ. of Newfoundland
Title:  "Group Gradings on Locally Finite Algebras"

April 11, 2008 (Friday), at 4:00 P.M. in Levan 201, (Colloquium Talk)
Speaker: Yuri Bahturin, Moscow State University and Memorial Univ. of Newfoundland
Title:  "New Methods in the Theory of Group Graded Algebras"

April 16, 2008, at 3:30 P.M. in Levan 401, (Colloquium Talk)
Speaker: Bruce Sagan, NSF/Michigan State University
Title:  "Congruences for Combinatorial Sequences"

April 23, 2008, at 3:30 P.M. Room: SAC 545
Speaker: Jeff Bergen, DePaul University
Title: 
"Skew Power Series Rings"

April 30, 2008, at 3:30 P.M. Room: Levan 401
Speaker: Jeff Bergen, DePaul University
Title:  "Abstract Algebra Meets Trigonometry - Is This Acute Title Or Am I Being Obtuse?”

May 7, 2008, at 3:30 P.M. Room: Levan 401
Speaker: Tony Giaquinto, Loyola University of Chicago
Title:  “Small Functionals for Frobenius Lie Algebras “

May 14, 2008, at 3:30 P.M. in Room: Levan 401
Speaker: Yang Zhang, DePaul University
Title: 
Skew Polynomials in Computer Algebra”

May 21, 2008, at 3:30 P.M. in Room: Levan 401 (Colloquium Talk)
Speaker: Earl Taft, Rutgers University
Title:  “One-Sided Hopf Algebras and the Boson-Fermion Correspondence”

May 29, 2008 (Thursday), at 3:00 P.M. in Room: Levan 305
Speaker: Susan Montgomery, University of Southern California
Title:  “
Representations of some Hopf algebras associated to the symmetric group S_n

May 30, 2008 (Friday), at 3:30 P.M. in Levan 201 (Colloquium Talk)
Speaker: Susan Montgomery, University of Southern California
Title:  “
Orthogonal representations of Hopf algebras”

June 4, 2008, at 3:30 P.M. in Room: TBA
Speaker: Elliot Krop, Loyola University of Chicago
Title: “How many edge-colors for almost-rainbow $K_5$s?” 

WINTER 2008


January 30, 2008 at 3:30 P.M. in SAC 545
Speaker: Stefan Catoiu, DePaul University
Title:  " An introduction to diagram algebras I "

February 6, 2008 at 3:30 P.M. in SAC 545
Speaker: Stefan Catoiu, DePaul University
Title:  " An introduction to diagram algebras II "

February 13, 2008, at 3:30 P.M. in SAC 545
Speaker: Leonid Krop, DePaul University
Title:  " Representations of Hopf algebras I "

February 20, 2008, at 3:30 P.M. in SAC 545
Speaker: Leonid Krop, DePaul University
Title:  " Representations of Hopf algebras II "

February 27, 2008, at 3:30 P.M. in SAC 545
Speaker: Leonid Krop, DePaul University
Title:  " Representations of Hopf algebras III "

March 5, 2008, at 3:30 P.M. in Levan 503
Speaker: Dijana Jakelic, UIC
Title:  "Finite-dimensional representations of hyper loop algebras"


March 10, 2008 at 3:30 P.M. in Levan 401
Speaker: Mona Mocanasu, Northwestern University
Title:  " Borel-Moore Homologies for Algebriac Schemes "


Fall 2007:

October 3, 2007 at 3:30 P.M. in Levan 406 (Colloquium Talk)
Speaker: Nicolas Andruskiewitsch, University of Cordoba, Argentina
Title“A Gentle Introduction to Nichols Algebras and Their Uses”
 
 
October 4, 2007 (Thursday) at 3:30
Speaker: Nicolas Andruskiewitsch, University of Cordoba, Argentina
Title"On pointed Hopf algebras associated to the symmetric groups" 

October 10, 2007 at 3:30 P.M. in Levan 406
Speaker:   Kiryl Tsishchanka, DePaul University
Title
"On integer polynomials that are optimally small at a given algebraic point"

October 17, 2007 at 3:30 P.M. in Levan 504 (Colloquium Talk)
Speaker: Donald Passman, University of Wisconsin-Madison
Title
"Group Rings of Infinite Groups"

October  24, 2007 at 3:30 P.M. in SAC 545
Speaker:
Allan Berele, DePaul University
Title
" Classification of identities of Incidence Algebras "

November 6, 2007 at 3:30 in Levan 501 (Colloquium Talk)
Speaker: Stephen Doty, Loyola University of Chicago
Title
" Constucting quantum groups via finite-dimensional algebras "