Communications in Algebra· 2026Q2
Leibniz bialgebras constructed by tensor product from Lie bialgebras and Perm bialgebras
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- 2026year
Short summary
Researchers constructed Leibniz bialgebra structures on the tensor product of Lie and perm algebras, proving this structure inherits properties like coboundary or quasi-triangular nature from the perm bialgebra.
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Key points
- Leibniz algebra structure exists on the tensor product of a Lie algebra and a perm algebra.
- This structure can be elevated to a Leibniz bialgebra.
- The tensor product of a quadratic Lie algebra and a perm bialgebra yields a Leibniz bialgebra.
- Coboundary, quasi-triangular, triangular, and factorizable properties are inherited from the perm bialgebra.
- An infinite-dimensional Leibniz bialgebra is constructed from a finite-dimensional Lie bialgebra and a quadratic Z-graded perm algebra.
AI-generated from the title and abstract; the full text is not read.
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 Z-graded perm algebra. Quasi-triangular and triangular infinite-dimensional Leibniz bialgebras are considered.
The authors' abstract, as published at the source. Communications in Algebra, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics