
Journal of Lie Theory 24 (2014), No. 1, 225258 Copyright Heldermann Verlag 2014 Composition Series of gl(m) as a Module for its Classical Subalgebras over an Arbitrary Field Martin Chaktoura Dept. of Mathematics and Statistics, University of Regina, 3737 Wascana Pkwy, Regina, SK S4S 0A2, Canada martin_chaktoura@yahoo.com.ar Fernando Szechtman Dept. of Mathematics and Statistics, University of Regina, 3737 Wascana Pkwy, Regina, SK S4S 0A2, Canada fernando.szechtman@gmail.com [Abstractpdf] \def\gl{{\frak gl}} Let $F$ be an arbitrary field and let $f\colon V\times V\to F$ be a nondegenerate symmetric or alternating bilinear form defined on a finite dimensional vector space over $F$. Let $L(f)$ be the subalgebra of $\gl(V)$ formed by all skewadjoint endomorphisms with respect to $f$. We find a composition series for the $L(f)$module $\gl(V)$ and furnish multiple identifications for its composition factors. Keywords: Lie algebra, bilinear form, irreducible module, composition series. MSC: 17B10; 17B05 [ Fulltextpdf (407 KB)] for subscribers only. 