USA Algebra SeminarSpring 2005 

Click on the title of a talk for the abstract (if available).
Date 
Speaker 
Topic 
Friday January 21 
Joerg Feldvoss 
Lie algebras and universal enveloping algebras

Friday January 28 
Joerg Feldvoss 
Prime ideals in noncommutative 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 
KazhdanLusztig 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 
KazhdanLusztig polynomials II 
Friday April 8 
Cornelius Pillen 
KazhdanLusztig 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 rth 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 rth 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 wellunderstood 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 
KazhdanLusztig polynomials IV 