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)
| NAME |
AFFILIATION |
| 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
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