Speaker: Donald Barnes (University of Sydney) Time: 12-13 Venue: Carslaw 375 Title: Faithful completely reducible representation of modular Lie algebras. Abstract: The Ado-Iwasawa Theorem asserts that a finite-dimensional Lie algebra L over a field F has a finite-dimensional faithful module V . There are several extensions asserting the existence of such a module V with various additional properties. In particular, Jacobson has proved that if the field F has characteristic p>0, then there exists a completely reducible such module V . I prove that if L is of dimension n over F of characteristic p, then L has a faithful completely reducible module V with dim(V) bounded by p^(n^2-1).