Description de la structure de certaines superalgèbres de Lie quadratiques via la notion de $T^*$-extension

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dc.creatorBajo, Ignacio
dc.creatorBenayadi, Said
dc.creatorBordemann, Martin
dc.date2000-02-17
dc.date.accessioned2026-07-07T04:33:56Z
dc.date.available2026-07-07T04:33:56Z
dc.descriptionIn this note we introduce the notion of $T^*-$extension $T^*{\mathfrak g}$ of a Lie superalgebra ${\mathfrak g}$, i.e. an extension of ${\mathfrak g}$ by its dual space ${\mathfrak g}^*$. The natural pairing induces on $T^*{\mathfrak g}$ an even supersymmetric nondegenerate bilinear form $B$ which is invariant ($B([X,Y],Z)=B(X,[Y,Z])$ for all $X,Y,Z \in T^*{\mathfrak g}$), i.e. the structure of a quadratic (or metrised or orthogonal) Lie superalgebra. These extensions can be classified by the third even scalar cohomology group of ${\mathfrak g}$. Moreover, we show that all finite-dimensional quadratic Lie superalgebras ${\mathfrak a}={\mathfrak a}_{\bar{0}} \oplus {\mathfrak a}_{\bar{1}}$ which are either nilpotent, or solvable and such that $[{\mathfrak a}_{\bar{1}},{\mathfrak a}_{\bar{1}}]\subset [{\mathfrak a}_{\bar{0}},{\mathfrak a}_{\bar{0}}]$ can be constructed by means of a $T^*-$extension in the case of an algebraically closed field of characteristic zero.
dc.descriptionLATEX 2e, amssymb, 6 pages, main body of the text in French, abridged English version included
dc.identifierhttps://arxiv.org/abs/math/0002146
dc.identifierhttp://arxiv.org/abs/math/0002146
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58715
dc.subjectQuantum Algebra
dc.subjectRings and Algebras
dc.subject15A63, 17B05, 17B30, 17B56
dc.titleDescription de la structure de certaines superalgèbres de Lie quadratiques via la notion de $T^*$-extension
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