In order to induce the associative classical Yang-Baxter equations of any weight,we present the notion of an antisymmetric infinitesimal(ASI)bialgebra of weightλ,extending the ASI bialgebras to any weight.Meanwhile,w...In order to induce the associative classical Yang-Baxter equations of any weight,we present the notion of an antisymmetric infinitesimal(ASI)bialgebra of weightλ,extending the ASI bialgebras to any weight.Meanwhile,we consider the BiHomdeformation of the bialgebra above,which leads to the major research object that we need:nonhomogeneous associative BiHom-classical Yang-Baxter equations(abhcYBes).Subsequently,we focus on the characterizations and constructions of abhcYBes from generalized O-operators and weighted Rota-Baxter operators,which can be seen as a generalization of the main results in[Adv.Theor.Math.Phys.26(2022)19652009].展开更多
基金supported by National Natural Science Foundation of China(Nos.12471033,12201188,12001174)Natural Science Foundation of Henan Province(No.242300421389)+1 种基金China Postdoctoral Science Foundation(No.2022M711076)Postdoctoral Research Grant in Henan Province(No.202103090).
文摘In order to induce the associative classical Yang-Baxter equations of any weight,we present the notion of an antisymmetric infinitesimal(ASI)bialgebra of weightλ,extending the ASI bialgebras to any weight.Meanwhile,we consider the BiHomdeformation of the bialgebra above,which leads to the major research object that we need:nonhomogeneous associative BiHom-classical Yang-Baxter equations(abhcYBes).Subsequently,we focus on the characterizations and constructions of abhcYBes from generalized O-operators and weighted Rota-Baxter operators,which can be seen as a generalization of the main results in[Adv.Theor.Math.Phys.26(2022)19652009].
