SMS scnews item created by Kevin Coulembier at Wed 23 Mar 2016 1001
Type: Seminar
Distribution: World
Expiry: 20 Apr 2016
Calendar1: 1 Apr 2016 1200-1300
CalLoc1: Carslaw 375
CalTitle1: Faithful completely reducible representation of modular Lie algebras
Auth: kevinc@pkevinc.pc (assumed)

# 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).


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