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On Deformations of n-Lie Algebras

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Non-Associative and Non-Commutative Algebra and Operator Theory

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 160))

Abstract

The aim of this paper is to review the deformation theory of n-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base. Moreover, we discuss degenerations and quantization of n-Lie algebras.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, Université de Haute-Alsace, Informatique et Applications 4 rue des Frères Lumière, 68093, Mulhouse, France

    Abdenacer Makhlouf

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  1. Abdenacer Makhlouf
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  1. Departement de Mathematiques et Informatique, Faculté des Sciences et Techniques, Université Cheikh Anta Diop, Dakar, Senegal

    Cheikh Thiécoumbe Gueye

  2. Department of Álgebra, Geometría y Topología, Facultad de Ciencias, Universidad de Málaga, Málaga, Spain

    Mercedes Siles Molina

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Makhlouf, A. (2016). On Deformations of n-Lie Algebras. In: Gueye, C., Molina, M. (eds) Non-Associative and Non-Commutative Algebra and Operator Theory. Springer Proceedings in Mathematics & Statistics, vol 160. Springer, Cham. https://doi.org/10.1007/978-3-319-32902-4_4

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