Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Description de la structure de certaines superalg\`ebres de Lie
  quadratiques via la notion de $T^*$-extension   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.

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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol