Poisson Polynomial Rings

Abstract

Let A be a Poisson algebra with Poisson bracket {·, ·} _A and let α,δ be linear maps from A into itself. Here we find a necessary and sufficient condition for the pair (α,δ) such that the polynomial ring A[x] has the Poisson bracket

for all a, b ∈ A and construct a class of Poisson algebras including the coordinate rings of Poisson 2 × 2-matrices and Poisson symplectic 4-space.

Keywords:

• Derivation
• Poisson algebra

2000 Mathematics Subject Classification:

• Primary 17B63
• Secondary 16W25

ACKNOWLEDGMENT

The author is supported by the Korea Research Foundation Grant, KRF-2002-015-CP0010.

Notes

Communicated by T. Lenagan.