Cohomology and Abelian Extensions of 3-Bihom-Lie Algebras

Abstract

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.

Keywords

3-Bihom-Lie algebras / cohomology / abelian extensions / generalized derivations

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RIGHTS & PERMISSIONS

Peking University