Philippe Gille

Torsors and classification of multiloop Lie algebras

Abstract. Our goal is to classify twisted toroidal Lie algebras namely Lie algebras which look like a simple complex Lie algebra g extended to a Laurent polynomial ring R. We shall discuss mainly the case of the Lie
algebra g=sl(n) which relates to projective representations of finite abelian groups, quantum tori and Brauer groups of henselian fields. This is a report on joint work with Arturo Pianzola.