Abstract view
On the Theorem of the Primitive Element with Applications to the Representation Theory of Associative and Lie Algebras


Published:20140403
Printed: Dec 2014
Leandro Cagliero,
CIEMCONICET, FAMAFUniversidad Nacional de Córdoba, Córdoba, Argentina.
Fernando Szechtman,
Department of Mathematics and Statistics, University of Regina, Regina, SK
Abstract
We describe of all finite
dimensional uniserial representations of a commutative associative
(resp. abelian Lie) algebra over a perfect (resp. sufficiently
large perfect) field. In the Lie case the size of the field
depends on the answer to following question, considered and solved
in this paper. Let $K/F$ be a finite separable field extension
and
let $x,y\in K$. When is $F[x,y]=F[\alpha x+\beta y]$ for some
nonzero elements $\alpha,\beta\in F$?