University of Sydney Algebra Seminar

Anne Moreau (Université de Poitiers)

Friday 25 November, 12-1pm, Place: Carslaw 375

Mishchenko-Fomenko algebras and nilpotent bicone

Let \(\mathfrak{g}\) be a complex semisimple algebra. We consider the Mishchenko-Fomenko subalgebra at a regular element \(x\). It is a maximal Poisson-commutative subalgebra of \(S(\mathfrak{g})\), constructed by the so-called argument shift method. Moreover, it is a polynomial algebra. We show that the free generators of this algebra form a regular sequence. This generalizes a result of Ovsiensko (for \(\mathfrak{sl}_n\) and x semisimple regular). Our proof is related to geometrical properties of the nilpotent bicone. In this talk, I will explain this and discuss some open questions.