2007-10-19

Victor Protsak, Cornell University

Elementary divisors for the general linear algebra

The universal enveloping algebra of gl(n) may be viewed as a noncommutative analogue of the polynomial functions on the space of n by n matrices, and it turns out that many classical notions and results of linear algebra (the characteristic polynomial and the minimal polynomial, the Cayley-Hamilton theorem) admit natural noncommutative counterparts. The Yangian of gl(n) plays an important if hidden role in the development of the theory. We will discuss a family of polynomials called "quantum invariants" that offer an alternative approach to the classification of completely prime primitive ideals in the spirit of the theory of elementary divisors.