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Journal of Lie Theory 32 (2022), No. 4, 1171--1186
Copyright Heldermann Verlag 2022

Weakly Associative and Symmetric Leibniz Algebras

Elisabeth Remm
(1) Université de Haute-Alsace, IRIMAS UR 7499, Mulhouse, France
(2) Université de Strasbourg, France

We study a special class of weakly associative algebras: the symmetric Leibniz algebras. We describe the structure of the commutative and skew-symmetric algebras associated with the polarization-depolarization principle. We also give a structure theorem for the symmetric Leibniz algebras and we describe the low dimensional classification. We finally study formal deformations in the context of deformation quantization.

Keywords: Weakly associative algebras, nonassociative algebras, symmetric Leibniz algebras, deformation quantization.

MSC: 17A30,17A32,53D55.

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