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Hom- -Operators and Hom-Yang-Baxter Equations

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  • Yuanyuan Chen
  • Liangyun Zhang

Abstract

In Hom-Lie set, we introduce the concept of Hom- -operators and study its relation with classical Hom-Yang-Baxter equation, as well as left-symmetric Hom-algebras. We construct the corresponding relation between left-symmetric Hom-algebras and Hom-1-cocycles, which are both related to classical Hom-Yang-Baxter equation. Moreover, in Hom-algebra setting, we establish the equivalent relationship between AHYBE (associative Hom-Yang-Baxter equations) and -operators on Frobenius monoidal Hom-algebras.

Suggested Citation

  • Yuanyuan Chen & Liangyun Zhang, 2015. "Hom- -Operators and Hom-Yang-Baxter Equations," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-11, August.
    • Handle: RePEc:hin:jnlamp:823756
    DOI: 10.1155/2015/823756
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    Cited by:

    1. Shuangjian Guo & Shengxiang Wang & Xiaohui Zhang, 2022. "The Classical Hom–Leibniz Yang–Baxter Equation and Hom–Leibniz Bialgebras," Mathematics, MDPI, vol. 10(11), pages 1-15, June.

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