Weak Leibniz algebras and transposed Poisson algebras

AskarDzhumadil'daev

Weak Leibniz algebras and transposed Poisson algebras

Rings and Algebras 2023-08-30 v1

Authors: AskarDzhumadil'daev

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.

Keywords

weak leibniz algebra transposed poisson algebra operad self-dual koszul polarization

Cite

@article{arxiv.2308.15018,
  title  = {Weak Leibniz algebras and transposed Poisson algebras},
  author = {AskarDzhumadil'daev},
  journal= {arXiv preprint arXiv:2308.15018},
  year   = {2023}
}

Comments

10 pages

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