Abstract:
An algebra with the identities
$[a,b]c=2a(bc)-2b(ac)$
and
$a[b,c]=2(ab)c-2(ac)b$
is called a weak Leibniz algebra.
It is shown that any weak Leibniz operad is
self-dual and not Koszul.
It is also proved that the polarization of any weak Leibniz algebra is a
transposed Poisson algebra and vice
versa, the depolarization of any transposed Poisson algebra is a weak Leibniz algebra.
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