# Reflection Groups and Rigidity of Quadratic Poisson Algebras

@article{Gaddis2021ReflectionGA, title={Reflection Groups and Rigidity of Quadratic Poisson Algebras}, author={Jason Gaddis and Padmini Veerapen and Xinting Wang}, journal={Algebras and Representation Theory}, year={2021} }

In this paper, we study the invariant theory of quadratic Poisson algebras. Let G be a finite group of the graded Poisson automorphisms of a quadratic Poisson algebra A. When the Poisson bracket of A is skew-symmetric, a Poisson version of the Shephard-Todd-Chevalley theorem is proved stating that the fixed Poisson subring A^G is skew-symmetric if and only if G is generated by reflections. For many other well-known families of quadratic Poisson algebras, we show that G contains limited or even…

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