# A remark on Mishchenko-Fomenko algebras and regular sequences

## TL;DR

This paper proves that the free generators of Mishchenko-Fomenko subalgebras form a regular sequence, using geometric properties of the nilpotent bicone, extending previous results beyond type A.

## Contribution

It introduces a new geometric approach to show the regularity of generators in Mishchenko-Fomenko algebras for complex reductive Lie algebras.

## Key findings

- Generators form a regular sequence at regular elements
- Approach based on geometric properties of the nilpotent bicone
- Extends previous results beyond type A

## 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.