Journal of Lie Theory

no. 4
Weakly Associative and Symmetric Leibniz Algebras
Journal of Lie Theory, Volume 32 (2022) no. 4, pp. 1171-1186
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.
DOI: 10.5802/jolt.1270
Classification: 17A30,17A32,53D55
Keywords: Weakly associative algebras, nonassociative algebras, symmetric Leibniz algebras, deformation quantization 
@article{JOLT_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},
     doi = {10.5802/jolt.1270},
     zbl = {1528.17003},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1270/}
}
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E. Remm. Weakly Associative and Symmetric Leibniz Algebras. Journal of Lie Theory, Volume 32 (2022) no. 4, pp. 1171-1186. doi: 10.5802/jolt.1270

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