Seminar in Algebraic Geometry and Number Theory

Abstract: I will present a construction of the first Weyl algebra, generated by two elements p and q modulo the relation pq-qp=1, from the Lie algebra sl(2). The construction can be generalised from sl(2) to any Kac--Moody algebra or, more generally, to any contragredient Lie algebra with a given integer-grading, but the generalised Weyl algebras will not be associative. Nevertheless, by commutators they give rise to new Lie algebras, which are not contragredient. This is joint work with Martin Cederwall, motivated by fundamental physics.