Invariant Lie polynomials in the representation of sl(2) and sl(3)
Hu Jiaxiong, Queens University
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).