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Weak Leibniz algebras and transposed Poisson algebras
Published 29 Aug 2023 in math.RA | (2308.15018v1)
Abstract: An algebra with identities $[a,b]c=2a(bc)-2b(ac), a[b,c]=2(ab)c-2(ac)b$ is called weak Leibniz. We show that weak Leibniz operad is self-dual and is not Koszul. We establish that polarization of any weak Leibniz algebra is transposed Poisson, and, conversely, polarization of any transposed Poisson algebra is weak Leibniz.
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