SMS scnews item created by Kevin Coulembier at Fri 15 Feb 2019 1705
Type: Seminar
Modified: Thu 28 Mar 2019 1008
Distribution: World
Expiry: 17 May 2019
Calendar1: 5 Apr 2019 1200-1300
CalLoc1: Carslaw 375
CalTitle1: Algebra Seminar: Faithful irreducible representations of modular Lie algebras
Auth: kevinc@10.17.64.168 (kcou7211) in SMS-WASM

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.


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