Algebra Seminar: Moreau -- Mishchenko-Fomenko algebras and nilpotent bicone

Anne Moreau (Universite de Poitiers) 

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

Mishchenko-Fomenko algebras and nilpotent bicone 

Let 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(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 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.