Reduction of Complex Poisson Manifolds

Joana Margarida Nunes da Costa

Abstract: In this paper we define the reduction of complex Poisson manifolds and we present a reduction theorem. We give an example of reduction on the dual of a complex Lie algebra with its complex Lie-Poisson structure. In this example the reduction is obtained by the action of a complex Lie subgroup of $SL(2,\C)$ on $sl^{*}(2,\C)$. Finally, we establish a relationship between complex and real Poisson reduction.

Keywords: Complex Poisson manifold; Poisson reduction.

Classification (MSC2000): 53C12, 53C15, 58F05

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