MITACS Seminar Series on Mathematics of Computer Algebra and Analysis

Invariant Lie polynomials in the representation of sl(2) and sl(3).

Jiaxiong Hu, Queens Univerity, Kingston, Ontario.

Thursday January 7th, 2010, at 12:30pm in K9509.


In this talk, I will focus on the nonassociative algebra of invariant
polynomials, which is rarely studied in invariant theory. I will introduce how
to compute the nonassociative invariants (invariant Lie polynomials) in the
representations of sl(2) and sl(3), where L is a free Lie algebra generated by
2 and 3 elements respectively. The rapid growth of the number of Lie invariants
of degree mr as a function of m, where r is the number of the free generators
(variables), suggests that the ring of the Lie invariants in r variables
probably can not be generated by a finite number of invariants (nobody proved it).
Due to heavy calculation task, computer algebra needs to come into play.

This is a joint work with Murray Bremner (University of Saskatchewan).