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Journal of Lie Theory 16 (2006), No. 3, 539--560 Copyright Heldermann Verlag 2006 Lie Superalgebras Based on a 3-Dimensional Real or Complex Lie Algebra Isabel Hernández Centro de Investigacion en Matematicas, Apdo. Postal 402, C.P. 36000 Guanajuato, Gto., Mexico isabel@cimat.mx Gil Salgado Centro de Investigacion en Matematicas, Apdo. Postal 402, C.P. 36000 Guanajuato, Gto., Mexico salgado@cimat.mx Oscar Adolfo Sánchez-Valenzuela Centro de Investigacion en Matematicas, Apdo. Postal 402, C.P. 36000 Guanajuato, Gto., Mexico adolfo@cimat.mx [Abstract-pdf] \def\g{{\frak g}} We give a complete classification of real and complex Lie superalgebras $\g_0\oplus\g_1$, for which $\g_0$ is a $3$-dimensional Lie algebra, and $\g_1$ is $\g_0$ itself under the adjoint representation. Keywords: Lie superalgebras, adjoint representation, symmetric equivariant maps. MSC: 17B70, 81R05; 15A21, 15A63, 17B81 [ Fulltext-pdf (237 KB)] for subscribers only. |