论文标题
反射组和二次泊松代数的刚度
Reflection Groups and Rigidity of Quadratic Poisson Algebras
论文作者
论文摘要
在本文中，我们研究了二次泊松代数的不变理论。让G为二次泊松代数A的分级泊松自动形态。对于许多二次泊松代数的许多知名家庭，我们表明G包含有限甚至没有反思。这种泊松刚度的结果可确保相应的固定泊松托管a^g与A作为泊松代数的同构不是同构，除非g是微不足道的。
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 no reflections. This kind of Poisson rigidity result ensures that the corresponding fixed Poisson subring A^G is not isomorphic to A as Poisson algebras unless G is trivial.
