Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 25 (2015), No. 2, 535--552Copyright 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 isabelie.hdez@gmail.com [Abstract-pdf] \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 [ Fulltext-pdf  (326  KB)] for subscribers only.