In the case of Lie algebras, the left (resp. right) invariance of bilinear forms is equivalent to the invariance (or associativity) of these forms. However, it is not the case for Leibniz algebras. In this talk, we will give some results on the structures of Leibniz algebras which are provided with symmetric non-degenerate bilinear forms which are either left (resp. right) invariant or associative.
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