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Representations of Leibniz Algebras

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Abstract

In this paper we prove that every irredicuble representation of a Leibniz algebra can be obtained from irreducible representations of the semisimple Lie algebra from the Levi decomposition. We also prove that - in general - for (semi)simple Leibniz algebras it is not true that a representation can be decomposed to a direct sum of irreducible ones.

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Authors and Affiliations

  1. Institute of Mathematics, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117, Budapest, Hungary

    A. Fialowski & É. Zs. Mihálka

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  1. A. Fialowski
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  2. É. Zs. Mihálka
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Correspondence to A. Fialowski.

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Presented By Anne Schilling.

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Fialowski, A., Mihálka, É.Z. Representations of Leibniz Algebras. Algebr Represent Theor 18, 477–490 (2015). https://doi.org/10.1007/s10468-014-9505-8

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  • DOI: https://doi.org/10.1007/s10468-014-9505-8

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