Geodesic
Weakly Associative and Symmetric Leibniz Algebras
Journal of Lie theory, Tome 32 (2022) no. 4, pp. 1171-1186
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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.
Classification : 17A30,17A32,53D55
Mots-clés : Weakly associative algebras, nonassociative algebras, symmetric Leibniz algebras, deformation quantization 
@article{JLT_2022_32_4_JLT_2022_32_4_a12,
     author = {E. Remm},
     title = {Weakly {Associative} and {Symmetric} {Leibniz} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {1171--1186},
     year = {2022},
     volume = {32},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2022_32_4_JLT_2022_32_4_a12/}
}
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E. Remm. Weakly Associative and Symmetric Leibniz Algebras. Journal of Lie theory, Tome 32 (2022) no. 4, pp. 1171-1186. http://geodesic.mathdoc.fr/item/JLT_2022_32_4_JLT_2022_32_4_a12/