uOttawa Mathematics

69th Algebra Day

Ottawa-Carleton Institute of Mathematics and Statistics

Conference Poster
Carleton Mathematics

Saturday, April 14, 2012
Department of Mathematics and Statistics,
University of Ottawa

Organizer : Erhard Neher

Conference Schedule

10:00 Coffee

10:30 Holger Petersson
(FernUniversität Hagen)
Moufang sets and the problem of commuting U-operators in Jordan algebras

Moufang sets, i.e., split BN-pairs (= Tits systems) of rank one, are known since the work of deMedts and Weiss to be intimitely connected with Jordan division rings. Following Segev and Tent, I will use this connection to translate a natural question about Moufang sets into an as yet unsolved problem for Jordan algebras. Partial solutions to the problem will be presented, and speculations about an answer in general will be offered.

11:45 Jose Malagon-Lopez
(University of Ottawa)
Exponents and formal group rings

Given the weight lattice Λ of a crystallographic root system with Weyl group W, the exponent of the W-action on Λ measures how far is the the ring of W-invariants of Sym* (Λ)W from being a polynomial ring in the generator set of ℕ[Λ]W. In this talk we extend this notion to the case of a formal group ring. This is joint work with K. Zainoulline.

12:30 Lunch
13:30 Alex Hoffnung
(University of Ottawa)
Hecke algebras and cohomology

Hecke algebras are well-known, in part, for their joint interpretations as both algebraic and geometric objects. For example, the affine Hecke algebra can be constructed geometrically via K-theory. In this talk I will discuss a general approach to Hecke algebras using axioms of oriented cohomology theories and related objects called formal group algebras. This approach leads to a general framework which specializes to known geometric constructions of the Hecke algebra and related algebraic objects. This is joint work with J. Malagon-Lopez, A. Savage, and K. Zainoulline.

14:15 Zinovy Reichstein
(University of British Columbia)
Simplifying polynomials by Tschirnhaus transformations: old and new

In this talk I will revisit the classical topic of polynomial equations (in one variable) and Tschirnhaus transformations. I will discuss 19th century theorems of Hermite, Joubert and Klein, recent results in this area, and several open problems.

15:30 Coffee

16:00 Elizabeth Dan-Cohen
(Louisiana State University)
A Koszul category of representations of finitary Lie algebras

We find an interesting category of representations of the three simple finitary Lie algebras. The modules in question are weight modules for every splitting Cartan subalgebra. We describe the injective modules in this category, and show that the category is anti-equivalent to the category of locally unitary finite-dimensional modules over a direct limit of finite-dimensional Koszul algebras. The talk is based on joint work with Ivan Penkov and Vera Serganova.

18:30 Chinese Dinner

Participants may also be interested in the Fields Institute workshop Exceptional Algebras and Groups April 19-22, 2012;