Leibniz bialgebras constructed by tensor product from Lie bialgebras and perm bialgebras

Bo Hou; Ru Li

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arXiv · 2608.22166

Leibniz bialgebras constructed by tensor product from Lie bialgebras and perm bialgebras

Bo Hou·Ru Li

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Abstract

The construction problem of Leibniz bialgebras from Lie bialgebras and perm bialgebras is considered in this paper. We show that there is a Leibniz algebra structure on the tensor product of a Lie algebra and a perm algebra, and elevate this conclusion to the level of bialgebra. We prove that the tensor product of a quadratic Lie algebra and a perm bialgebra has a Leibniz bialgebra structure, and this Leibniz bialgebra structure is coboundary (resp. quasi-triangular, triangular, factorizable) if the original perm bialgebra is coboundary (resp. quasi-triangular, triangular, factorizable). Moreover, we constructed an infinite-dimensional Leibniz bialgebra using the tensor product of a finite-dimensional Lie bialgebra and a quadratic $\bz$-graded perm algebra. Quasi-triangular and triangular infinite-dimensional Leibniz bialgebras are considered.

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Bo Hou, Ru Li. 2026-08-23. Leibniz bialgebras constructed by tensor product from Lie bialgebras and perm bialgebras. https://arxiv.org/abs/2608.22166

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