Weak Leibniz Algebras

2025

Closed access Metadata (CSL-JSON)
DOI 10.1134/s0001434625030204
Data confidence 70 medium
How this score is calculated

It is built from checkable properties of the record itself: whether the article has a DOI, how many independent sources confirmed its data, whether the required fields are filled in, and how recent the latest confirmation is. Disagreement between sources and a missing identifier lower it. A value of 80 or above means the record was published without further checking; 60 to 79 means it is published at reduced confidence, with a manual check advisable. A record verified by an editor by hand is never pushed below 90 by a recalculation. This scores our data about the article, not the article itself.

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.