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<p>We introduce the notion of quasi-triangular mock-Lie bialgebras and factorizable mock-Lie bialgebras. A quasi-triangular mock-Lie bialgebra can be constructed from solutions of the mock-Lie Yang-Baxter equation whose symmetric parts are invariant. A factorizable mock-Lie bialgebra leads to a factorization of the underlying mock-Lie algebra. We show that there is a one-to-one correspondence between factorizable mock-Lie bialgebras and quadratic Rota-Baxter mock-Lie algebras of nonzero weight. Finally, we construct quasi-triangular (resp. triangular, factorizable) Lie bialgebras from quasi-triangular (resp. triangular, factorizable) mock-Lie bialgebras by tensor product.</p>

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Quasi-Triangular Mock-Lie Bialgebras and the Induced Quasi-Triangular Lie Bialgebras

  • 期刊论文

  • 发表日期：

    2026年2月12日

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  • Zhanpeng Cui,
  • Bo Hou

摘要

We introduce the notion of quasi-triangular mock-Lie bialgebras and factorizable mock-Lie bialgebras. A quasi-triangular mock-Lie bialgebra can be constructed from solutions of the mock-Lie Yang-Baxter equation whose symmetric parts are invariant. A factorizable mock-Lie bialgebra leads to a factorization of the underlying mock-Lie algebra. We show that there is a one-to-one correspondence between factorizable mock-Lie bialgebras and quadratic Rota-Baxter mock-Lie algebras of nonzero weight. Finally, we construct quasi-triangular (resp. triangular, factorizable) Lie bialgebras from quasi-triangular (resp. triangular, factorizable) mock-Lie bialgebras by tensor product.