Differential Invariant Algebras

Algebra Seminar
Monday, February 24, 2020 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 005
Peter Olver – University of Minnesota – olver@umn.eduhttp://www-users.math.umn.edu/~olver/
Anton Leykin

A classical theorem of Lie and Tresse states that the algebra of differential invariants of a Lie group or (suitable) Lie pseudo-group action is finitely generated.  I will present a fully constructive algorithm, based on the equivariant method of moving frames, that reveals the full structure of such non-commutative differential algebras, and, in particular, pinpoints generating sets of differential invariants as well as their differential syzygies. Some applications and outstanding issues will be discussed.