## University of Sydney Algebra Seminar

# Don Barnes (University of Sydney)

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

## Faithful irreducible representations of modular Lie algebras

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.