Abstract
Let (C, α) and (H, β) be Hom-bialgebras and ω: C ⊗H → H ⊗C a linear map. We introduce a Hom-ω-smash coproduct (C ω ⋈ H, γ) and give necessary and sufficient conditions for (C ω ⋈ H, γ) to be a Hom-bialgebra. We study the quasi-triangular structures over (C ω ⋈ H, γ) and show the necessary and sufficient conditions for (C ω ⋈ H, γ, R) to be a quasi-triangular Hom-Hopf algebra. As applications of our results, we introduce the concept of D(H)* and construct quasi-triangular structures over D(H)*.
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Supported by the National Natural Science Foundation of China (60873267), the Ningbo Natural Science Foundation of China (2011A610172), and K. C. Wang Magna Fund in Ningbo University.
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Zheng, Nf. The quasi-triangular structures over Hom-ω-smash coproduct Hopf algebras. Appl. Math. J. Chin. Univ. 31, 219–236 (2016). https://doi.org/10.1007/s11766-016-3046-3
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DOI: https://doi.org/10.1007/s11766-016-3046-3