Algebra Seminar: Barnes -- Faithful irreducible representations of modular Lie algebras

Don Barnes (University of Sydney) 

Friday 5 April, 12-1pm, Place: Carslaw 375 

Title: Faithful irreducible representations of modular Lie algebras 

Abstract: Let L be a finite-dimensional Lie algebra over a field F of non-zero
characteristic.  Jacobson has proved that L has a finite-dimensional faithful completely
reducible module.  I adapt Jacobson’s proof to show that if F is not algebraically
closed, then L has a finite-dimensional faithful irreducible module.  The argument also
gives for the algebraically closed case, a necessary and sufficient condition on L for
it to have a finite-dimensional faithful irreducible module.