The Lie Algebra Preserving A Degenerate Bilinear Form
Journal of Lie Theory, Tome 33 (2023) no. 2, pp. 477-495
Voir la notice de l'article provenant de la source Heldermann Verlag
Let k be an arbitrary field and d a positive integer. For each degenerate symmetric or antisymmetric bilinear form M on kd we determine the structure of the Lie algebra of matrices that preserve M, and of the Lie algebra of matrices that preserve the subspace spanned by M. We show that these Lie algebras are semidirect products of classical Lie algebras and certain representations, and determine their radicals, derived series and semisimple quotients. Our main motivation and application is to determine the structure of the graded Lie algebra of derivations of each commutative or graded commutative algebra with Hilbert polynomial 1+dt+t2. Some of our results apply to more general bilinear forms and graded algebras.
Classification :
17B05,13N15,17B70
Mots-clés : Graded algebras, graded Lie algebras, biliner forms, derivations
Mots-clés : Graded algebras, graded Lie algebras, biliner forms, derivations
Affiliations des auteurs :
James Waldron 1
James Waldron. The Lie Algebra Preserving A Degenerate Bilinear Form. Journal of Lie Theory, Tome 33 (2023) no. 2, pp. 477-495. http://geodesic.mathdoc.fr/item/JOLT_2023_33_2_a1/
@article{JOLT_2023_33_2_a1,
author = {James Waldron},
title = {The {Lie} {Algebra} {Preserving} {A} {Degenerate} {Bilinear} {Form}},
journal = {Journal of Lie Theory},
pages = {477--495},
year = {2023},
volume = {33},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2023_33_2_a1/}
}