ePrints

The Lie Algebra Preserving A Degenerate Bilinear Form

Lookup NU author(s): Dr James Waldron

Downloads

Full text for this publication is not currently held within this repository. Alternative links are provided below where available.

Abstract

© 2023 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.

Publication metadata

Author(s): Waldron J

Publication type: Article

Publication status: Published

Journal: Journal of Lie Theory

Year: 2023

Volume: 33

Issue: 2

Pages: 477-495

Online publication date: 01/01/2023

Acceptance date: 01/01/2023

ISSN (print): 0949-5932

Publisher: Heldermann Verlag

URL: https://www.heldermann.de/JLT/JLT33/JLT332/jlt33020.htm

Share