A remark on Mishchenko–Fomenko algebras and regular sequences

Anne Moreau ^[1]
1. [1] Laboratoire Paul Painlevé
  
  Laboratoire Paul Painlevé
  
  Arrondissement de Lille, Francia
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 3, 2018, págs. 2651-2657
Idioma: inglés
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Resumen
- 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.