Weak Leibniz algebras and transposed Poisson algebras

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.

arXiv comment10 pages

Cited by in corpus (1)

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