
School of Mathematics and Statistics
Don Barnes
University of Sydney
Cohomology of Fexcentric modules of a soluble Lie algebra
Friday 7th December, 121pm,
Carslaw 375.
The AdoIwasawa Theorem asserts that a finitedimensional Lie algebra
has a faithful finitedimensional module. I strengthen that result.
Let F be a saturated formation of soluble Lie algebras. Let
S in F be an ideal of the finitedimensional Lie
algebra L. I show that there exists a faithful
finitedimensional Lmodule which, as Smodule, is
Fhypercentral.
Taking the special case of the formation of supersoluble algebras,
this gives the existence of a representation of L in which
the supersoluble ideal S of L is represented by
upper triangular matrices.
