Weak Leibniz algebras and transposed Poisson algebras

AskarDzhumadil'daev

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 p…