Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 54, No. 4, pp. 467-476 (1997)

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Reduction of Complex Poisson Manifolds

Joana Margarida Nunes da Costa

Departamento de Matemática, Universidade de Coimbra,
Apartado 3008, 3000 Coimbra - PORTUGAL
E-mail: jmcosta@mat.uc.pt

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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Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.

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