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Selecta Mathematica

, Volume 24, Issue 3, pp 2651–2657 | Cite as

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.

Keywords

Mishchenko–Fomenko algebra Regular sequence Nilpotent bicone 

Mathematics Subject Classification

17B20 14B05 

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Notes

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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Laboratoire Paul Painlevé, CNRS U.M.R. 8524Villeneuve d’Ascq CedexFrance

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