Last updated: September 29, 2006

Northeastern University
Mathematics Department

Maurice Auslander
Distinguished Lectures*

October 5 - 6, 2006

Pierre Vogel
(University of Paris 7)


Date and Time
Location Titles
Thursday, Oct. 5, 4:30 - 5:30
315 Shillman Hall The Universal Lie Algebra
Friday, Oct. 6, 10:30 - 11:30
511 Lake Hall The Coefficient Ring of the Universal Lie Algebra

Social Program

Date and Time
Thursday, Oct. 5, 5:45 - 7:00
340 Egan
Thursday, Oct. 5, 7:30

Titles and Abstracts

  • Lecture 1   The Universal Lie Algebra
Abstract:     The properties of simple Lie algebras or simple Lie superalgebras can be globalized in a categorical way in order to produce an object called the universal Lie algebra. This object is an R-linear tensor category where R is a commutative ring. It is useful for understanding many properties of Lie algebras and representations of Lie algebras. It is also useful for producing finite type invariants of knots, links, and 3-dimensional manifolds. The coefficient ring R is highly unknown but a complete description of it is conjectured.

  • Lecture 2   The Coefficient Ring of the Universal Lie Algebra

Abstract:     The coefficient ring of the universal Lie algebra L is a graded commutative algebra Λ[δ],
where δ is in some sense the dimension of L and Λ is a graded algebra generated by trivalent diagrams. This algebra is essentially unknown but it captures all finite-typeinvariants of three-dimensional manifolds. Each simple Lie (super)-algebra over K produces a ring homomorphism from Λ to K, and Λ is known up to degree 10. I propose a conjecture, related to a conjecture of Deligne, giving a complete description of this algebra. I prove a part of this conjecture and show many consequences of it in the theory of quantum invariants in low-dimensional topology.

Concurrent Activities

Registered Participants (as of September 29, 2006)

Thomas Bruestle Bishop's University  and Universtity of Sherbrooke
Dieter Happel TU Chemnitz
Ivan Horozov Brandeis University
Kiyoshi Igusa Brandeis University
Naihuan Jing NCSU
Mark Kleiner Syracuse University
Alex Martsinkovsky Northeastern University
Jean-Philippe Morin University of Sherbrooke
Mara Neusel Texas Tech
Charles Paquette University of Sherbrooke
Pierre-Guy Plamondon University of Sherbrooke
Ralf Schiffler University of Massashusetts, Amherst
Gordana Todorov Northeastern University
Jerzy Weyman Northeastern University

To register or for further information, contact Alex Martsinkovsky alexmart >at< neu >dot< edu

Archive: 2005 2004 2003 2002

* Sponsored by Bernice Auslander