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

I. Hernández

doi:10.5802/jolt.849

I. Hernández

Journal of Lie Theory, Volume 25 (2015) no. 2, pp. 535-552

Abstract

\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.

Zbl

DOI: 10.5802/jolt.849

Classification: 17B20, 17B70, 81R05
Keywords: Lie superalgebras, reductive Lie algebras

@article{JOLT_2015_25_2_a11,
     author = {I. Hern\'andez},
     title = {Classification of {Lie} {Superalgebras} {Supported} over a {Reductive} {Lie} {Algebra} with {One-Dimensional} {Center} and a {Simple} {Lie} {Algebra} as a {First} {Derived} {Ideal}},
     journal = {Journal of Lie Theory},
     pages = {535--552},
     year = {2015},
     volume = {25},
     number = {2},
     doi = {10.5802/jolt.849},
     zbl = {1368.17010},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.849/}
}

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I. Hernández. Classification of Lie Superalgebras Supported over a Reductive Lie Algebra with One-Dimensional Center and a Simple Lie Algebra as a First Derived Ideal. Journal of Lie Theory, Volume 25 (2015) no. 2, pp. 535-552. doi: 10.5802/jolt.849

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