Weakly Associative and Symmetric Leibniz Algebras

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.

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