Algebra Seminar: Barnes -- Faithful completely reducible representation of modular Lie algebras

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).