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The algebraic and geometric classification of post-$3$-Lie algebras
A post-$3$-Lie algebra is a $3$-Lie algebra with an additional ternary multiplication, skew-symmetric in the first two arguments, related to the bracket by four compatibility identities. We give the algebraic and geometric classification of complex $2$- and $3$-dimensional post-$3$-Lie algebras and
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