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- W1666886959 abstract "In 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." @default.
- W1666886959 created "2016-06-24" @default.
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- W1666886959 date "2000-02-17" @default.
- W1666886959 modified "2023-09-22" @default.
- W1666886959 title "Description de la structure de certaines superalg`ebres de Lie quadratiques via la notion de $T^*$-extension" @default.
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