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<p>In this paper, we give the cohomology of 3-Bihom-Lie algebras and we show that an <i>α</i><sup>2</sup><i>β</i><sup>−1</sup>-derivation is a closed 1-Bihom-cochain with the adjoint representation. As an application, we introduce abelian extensions of 3-Bihom-Lie algebras and obtain that there is a one-to-one correspondence between equivalent classes of abelian extensions and the second cohomology group by closed 2-Bihom-cochains. Moreover, we introduce the notion of a generalized derivation of 3-Bihom-Lie algebras and we construct a new 3-Bihom-Lie algebra with a generalized derivation.</p>

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Cohomology and Abelian Extensions of 3-Bihom-Lie Algebras

  • 期刊论文

  • 发表日期：

    2025年6月5日

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  • Juan Li,
  • Liangyun Chen

摘要

In this paper, we give the cohomology of 3-Bihom-Lie algebras and we show that an α2β−1-derivation is a closed 1-Bihom-cochain with the adjoint representation. As an application, we introduce abelian extensions of 3-Bihom-Lie algebras and obtain that there is a one-to-one correspondence between equivalent classes of abelian extensions and the second cohomology group by closed 2-Bihom-cochains. Moreover, we introduce the notion of a generalized derivation of 3-Bihom-Lie algebras and we construct a new 3-Bihom-Lie algebra with a generalized derivation.