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- W3081542675 abstract "Let $k$ be an arbitrary field and $d$ a positive integer. For each degenerate symmetric or antisymmetric bilinear form $M$ on $k^{d}$ 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 $1+dt+t^{2}$. Some of our results apply to more general bilinear forms and graded algebras." @default.
- W3081542675 created "2020-09-08" @default.
- W3081542675 creator A5080899263 @default.
- W3081542675 date "2020-09-03" @default.
- W3081542675 modified "2023-09-27" @default.
- W3081542675 title "The Lie algebra preserving a degenerate bilinear form" @default.
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- W3081542675 hasPublicationYear "2020" @default.
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