Antisymmetric Infinitesimal Bialgebras of Any Weight and Related Associative Classical Yang-Baxter Equations

In order to induce the associative classical Yang-Baxter equations of any weight, we present the notion of an antisymmetric infinitesimal (ASI) bialgebra of weight [Formula: see text], extending the ASI bialgebras to any weight. Meanwhile, we consider the BiHom-deformation 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 [Formula: see text]-operators and weighted Rota-Baxter operators, which can be seen as a generalization of the main results in [Adv. Theor. Math. Phys. 26 (2022) 1965–2009].