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Journal of Lie Theory 25 (2015), No. 2, 535--552
Copyright Heldermann Verlag 2015

Classification of Lie Superalgebras Supported over a Reductive Lie Algebra with One-Dimensional Center and a Simple Lie Algebra as a First Derived Ideal

Isabel Hernández
Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brasil


\def\g{{\frak g}} \def\m{{\frak m}} \def\z{{\frak z}} It is the aim of this work to provide a concrete list of representatives of the isomorphism classes of finite-dimensional Lie superalgebras $\g = \g_0 \oplus \g_1$ supported over a reductive Lie algebra $\g_0=\m \oplus \z$, where $\m$ is a simple Lie algebra and $\z$, the center of $\g_0$, is one-dimensional. The classification given here does not impose the extra hypothesis that $\g_1$ be a completely reducible $\g_0$-module.

Keywords: Lie superalgebras, reductive Lie algebras.

MSC: 17B20, 17B70; 81R05

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