Geodesic
Composition Series of gl(m) as a Module for its Classical Subalgebras over an Arbitrary Field
Martin Chaktoura1 ; Fernando Szechtman1
1Dept. of Mathematics and Statistics, University of Regina, 3737 Wascana Pkwy, Regina, SK S4S 0A2, Canada
Journal of Lie Theory, Tome 24 (2014) no. 1, pp. 225-258

Voir la notice de l'article provenant de la source Heldermann Verlag

\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.
Classification : 17B10, 17B05
Mots-clés : Lie algebra, bilinear form, irreducible module, composition series

Martin Chaktoura  1   ; Fernando Szechtman  1

1 Dept. of Mathematics and Statistics, University of Regina, 3737 Wascana Pkwy, Regina, SK S4S 0A2, Canada 
Martin Chaktoura; Fernando Szechtman. Composition Series of gl(m) as a Module for its Classical Subalgebras over an Arbitrary Field. Journal of Lie Theory, Tome 24 (2014) no. 1, pp. 225-258. http://geodesic.mathdoc.fr/item/JOLT_2014_24_1_a10/
@article{JOLT_2014_24_1_a10,
     author = {Martin Chaktoura and Fernando Szechtman},
     title = {Composition {Series} of gl(m) as a {Module} for its {Classical} {Subalgebras} over an {Arbitrary} {Field}},
     journal = {Journal of Lie Theory},
     pages = {225--258},
     year = {2014},
     volume = {24},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2014_24_1_a10/}
}
TY  - JOUR
AU  - Martin Chaktoura
AU  - Fernando Szechtman
TI  - Composition Series of gl(m) as a Module for its Classical Subalgebras over an Arbitrary Field
JO  - Journal of Lie Theory
PY  - 2014
SP  - 225
EP  - 258
VL  - 24
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JOLT_2014_24_1_a10/
ID  - JOLT_2014_24_1_a10
ER  - 
%0 Journal Article
%A Martin Chaktoura
%A Fernando Szechtman
%T Composition Series of gl(m) as a Module for its Classical Subalgebras over an Arbitrary Field
%J Journal of Lie Theory
%D 2014
%P 225-258
%V 24
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2014_24_1_a10/
%F JOLT_2014_24_1_a10