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A remark on Mishchenko–Fomenko algebras and regular sequences

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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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  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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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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