USA Algebra Seminar 

  Spring 2005

The USA Algebra Seminar will meet on Fridays from  1:15 PM to 2:15 PM in  ILB 370.  Please let us know if you would like to give a talk or if you are interested in some specific topic. Everyone is welcome to attend.

Joerg Feldvoss, Cornelius Pillen

Click on the title of a talk for the abstract (if available).
Friday January 21
Joerg Feldvoss
Lie algebras and universal enveloping algebras
Friday January 28
Joerg Feldvoss
Prime ideals in non-commutative rings
Friday February 4
Joerg Feldvoss
Injective modules over noetherian rings
Friday February 11

No seminar
Friday February 18
Joerg Feldvoss
Injective modules over universal enveloping algebras
Friday February 25
Cornelius Pillen
Kazhdan-Lusztig polynomials I
Friday March 4

No seminar
Friday March 11
Mohamed Elhamdadi (University of South Florida)
Homological algebra of racks and quandles II
Friday March 18

No seminar (Spring break)
Friday March 25

No seminar
Friday April 1
Cornelius Pillen
Kazhdan-Lusztig polynomials II
Friday April 8
Cornelius Pillen
Kazhdan-Lusztig polynomials III
Thursday April 14
Brian Boe (University of Georgia)
Nilpotent matrices in Lie algebras (Colloquium in ILB 360)

It's easy to describe the set of n x n complex matrices whose r-th power is zero: each is conjugate (via an invertible matrix) to a Jordan canonical form matrix with all eigenvalues 0 and blocks of size at most r. In this talk I will discuss work done by the University of Georgia VIGRE Algebra Group on generalizations of this problem. We will consider an arbitrary simple algebraic group G over an algebraically closed field, along with certain embeddings of its Lie algebra g into n x n matrices, and describe the set of elements of g whose r-th power is zero, in terms of G conjugacy classes. As a corollary, when the characteristic is p, we obtain a description of the ``restricted nullcone'' of g (the case r=p), which is important in the study of Lie algebra cohomology. When p is a ``good prime'' (not too small), this verifies, by much more elementary methods, a 2003 result of Carlson, Lin, Nakano, and Parshall. And when p is ``bad'' (very small), our results are new. Most of the talk should be accessible to first year graduate students. I will discuss further applications and continuations of our work in my algebra seminar talk.

Friday April 15
Brian Boe (University of Georgia)
Support varieties for Lie algebras

Support varieties are geometric objects associated to cohomology rings and representations. In the case of modular representations of Lie algebras, it turns out that the supports are subvarieties of the (restricted) nullcone, a very concrete object with a rather well-understood structure. I will discuss recent work of the University of Georgia VIGRE Algebra Group in which we identified explicitly the support varieties of induced modules in the ``bad prime'' setting. This extends the verification by Nakano, Parshall, and Vella of a conjecture of Jantzen for ``good primes.''

Friday April 22
Cornelius Pillen
Kazhdan-Lusztig polynomials IV