Type: Seminar

Modified: Thu 28 Mar 2019 1008

Distribution: World

Expiry: 17 May 2019

CalTitle1: Algebra Seminar: Faithful irreducible representations of modular Lie algebras

Auth: kevinc@10.17.64.168 (kcou7211) in SMS-WASM

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.