7 papers
Differential perm bialgebras, differential perm Yang-Baxter equation, and their applications in related bialgebra structures
Ahuan Dong, Bo Hou
We introduce the differential perm bialgebras by generalizing the study of perm bialgebras to the context of differential perm algebras. They are characterized by the Manin triple…
Some constructions of antisymmetric infinitesimal bialgebras and their applications to Lie bialgebras
Bo Hou
In this paper, we mainly provide some methods for constructing antisymmetric infinitesimal (ASI) bialgebras and Lie bialgebras using Zinbiel bialgebras and diassociative bialgebras…
Construction of diassociative bialgebras from antisymmetric infinitesimal bialgebras and related algebra structures
Bo Hou, Ru Li
There is a diassociative algebra structure on the tensor product of an associative algebra and a perm algebra. In this paper, we elevate this conclusion to the level of bialgebra.W…
Leibniz bialgebras constructed by tensor product from Lie bialgebras and perm bialgebras
Bo Hou, Ru Li
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…
Lie bialgebras constructed from Zinbiel bialgebras and Leibniz bialgebras
Bo Hou, Yuanchang Lin
There is a Lie algebra structure on the tensor product of a Leibniz algebra and a Zinbiel algebra for the operads of Leibniz algebras and Zinbiel algebras are Koszul dual. In this…
Quasi-triangular dual pre-Poisson bialgebras and its connection with Poisson bialgebras
Bo Hou, Ru Li
In this paper, the notions of quasi-triangular and factorizable dual pre-Poisson bialgebras are introduced. A factorizable dual pre-Poisson bialgebra induces a factorization of the…
Affinization of Zinbiel bialgebras and pre-Poisson bialgebras, infinite-dimensional Poisson bialgebras
Yanhong Guo, Bo Hou
The purpose of this paper is to construct infinite-dimensional Poisson bialgebras by the affinization of pre-Poisson algebras. There is a natural Poisson algebra structure on the t…