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Journal of Lie Theory 16 (2006), No. 1, 131--138
Copyright Heldermann Verlag 2006

Symplectic Submanifolds and Symplectic Ideals

Sei-Qwon Oh
Department of Mathematics, Chungnam National University, Daejeon 305-764, Korea


Let $N$ be a Poisson manifold with global coordinate functions. We define a symplectic ideal of the ring $C^\infty(N)$ of smooth functions and investigate a relationship between symplectic submanifolds of $N$ and symplectic ideals of $C^\infty(N)$.

Keywords: Poisson algebra, symplectic submanifold, symplectic ideal.

MSC: 17B63; 53D05, 53D17

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