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A remark on Mishchenko–Fomenko algebras and regular sequences

Selecta Mathematica volume 24, pages 2651–2657 (2018)Cite this article

Abstract

In this note, we show that the free generators of the Mishchenko–Fomenko subalgebra of a complex reductive Lie algebra, constructed by the argument shift method at a regular element, form a regular sequence. This result was proven by Serge Ovsienko in the type A at a regular and semisimple element. Our approach is very different, and is strongly based on geometric properties of the nilpotent bicone.

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Acknowledgements

The author is very grateful to Tomoyuki Arakawa and Vyacheslav Futorny for submitting this problem to her attention. She thanks Jean-Yves Charbonnel very much for his useful remarks about this note. Finally, she wishes to thank the anonymous referee for his careful reading and judicious comments.

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Authors and Affiliations

  1. Laboratoire Paul Painlevé, CNRS U.M.R. 8524, 59655, Villeneuve d’Ascq Cedex, France

    Anne Moreau

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  1. Anne Moreau
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Correspondence to Anne Moreau.

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Moreau, A. A remark on Mishchenko–Fomenko algebras and regular sequences. Sel. Math. New Ser. 24, 2651–2657 (2018). https://doi.org/10.1007/s00029-017-0357-z

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  • DOI: https://doi.org/10.1007/s00029-017-0357-z

Keywords

  • Mishchenko–Fomenko algebra
  • Regular sequence
  • Nilpotent bicone

Mathematics Subject Classification

  • 17B20
  • 14B05