Tianshui Ma, Jie Li: Nonhomogeneous associative Yang-Baxter equations, 97-118


We introduce the notion of associative (BiHom-)Yang-Baxter pair of weight $(\lambda,\gamma)$ which can provide the solution to the double curved Rota-Baxter (BiHom-)system. Equivalent characterizations of (quasitriangular) covariant BiHom-bialgebra are given. We also prove that associative BiHom-Yang-Baxter equation of weight $-1$ can be obtained by the unitary quasitriangular covariant BiHom-bialgebra. At last, we present two approaches to construct (BiHom-)pre-Lie modules from Rota-Baxter (BiHom-) paired modules.

Key Words: Nonhomogeneous associative Yang-Baxter equations, Rota-Baxter system, covariant bialgebra.

2010 Mathematics Subject Classification: Primary 17B38; Secondary 16T10, 17A30, 17D30.

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