The Shephard-Todd-Chevalley Theorem gives conditions for the invariant ring of a polynomial ring to again be polynomial. However, this behaviour is rarely observed for non-commutative algebras. For example, the invariant ring of the first Weyl algebra by a finite group is not isomorphic to the first Weyl algebra. In this talk, I will discuss this rigidity in the context of quadratic Poisson algebras. A key example will be those Poisson polynomial algebras with skew-symmetric structure.
This is joint work with Padmini Veerapen and Xingting Wang.
This video is part of the Non-Associative Day in Online, run by the European Non-Associative Algebra Seminar series.
