Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 24 (2014), No. 1, 225--258Copyright 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 [Abstract-pdf] \def\gl{{\frak gl}} Let $F$ be an arbitrary field and let $f\colon V\times V\to F$ be a non-degenerate 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 skew-adjoint 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 [ Fulltext-pdf  (407  KB)] for subscribers only.