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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.

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Authors and Affiliations

  1. Division of Mathematical Methods in Physics, University of Warsaw, Hoża St. 74, Warsaw, 00-682, Poland

    Andriy Panasyuk

  2. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich St. 8, Warsaw, 00-950, Poland

    Andriy Panasyuk

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  1. Andriy Panasyuk
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Correspondence to Andriy Panasyuk.

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Partially supported by the Polish grant KBN 2 P03A 001 24.

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Panasyuk, A. Reduction by stages and the Raïs-type formula for the index of a Lie algebra with an ideal. Ann Glob Anal Geom 33, 1–10 (2008). https://doi.org/10.1007/s10455-007-9070-z

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  • DOI: https://doi.org/10.1007/s10455-007-9070-z

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