Geodesic
Weakly Associative and Symmetric Leibniz Algebras
Elisabeth Remm1, 2
1(1) Université de Haute-Alsace, IRIMAS UR 7499, Mulhouse, France
2(2) Université de Strasbourg, France
Journal of Lie Theory, Tome 32 (2022) no. 4, pp. 1171-1186

Voir la notice de l'article provenant de la source Heldermann Verlag

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

Elisabeth Remm  1 , 2

1 (1) Université de Haute-Alsace, IRIMAS UR 7499, Mulhouse, France
2 (2) Université de Strasbourg, France 
Elisabeth Remm. Weakly Associative and Symmetric Leibniz Algebras. Journal of Lie Theory, Tome 32 (2022) no. 4, pp. 1171-1186. http://geodesic.mathdoc.fr/item/JOLT_2022_32_4_a12/
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     author = {Elisabeth 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/JOLT_2022_32_4_a12/}
}
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