Annals of Global Analysis and Geometry

, Volume 33, Issue 1, pp 1–10 | Cite as

Reduction by stages and the Raïs-type formula for the index of a Lie algebra with an ideal

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Abstract

For a quite general class of Lie algebras with a nontrivial ideal we derive a formula for the index generalizing the Raïs formula for the index of semidirect products. The method of proof of our formula is based on the so-called “symplectic reduction by stages” scheme.

Keywords

Lie algebra Index of a Lie algebra Poisson reduction Reduction by stages 

Mathematical Subject Classification

22E60 53D20 
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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Division of Mathematical Methods in PhysicsUniversity of Warsaw00-682Poland
  2. 2.Institute of MathematicsPolish Academy of SciencesWarsawPoland

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