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arXiv · 2011.05560

Representations, extensions and deformations of $n$-BiHom-Lie algebras

Ismail Laraiedh
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Abstract

In this paper we define and discuss the representations of $n$-BiHom-Lie algebra. We also introduce $T_{\theta}$-extensions and $T_{\theta}^{\ast}$-extensions of $n$-BiHom-Lie algebras and prove the necessary and sufficient conditions for a $2m$-dimensional quadratic $n$-Bihom-Lie algebra to be isomorphic to a $T_{\theta}^{\ast}$-extension. Moreover, we develop the one-parameter formal deformations of $n$-BiHom-Lie algebras, and we proved that the first and second cohomology groups are suitable to the deformation theory involving infinitesimals, equivalent deformations, and rigidity

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Ismail Laraiedh. 2020-10-21. Representations, extensions and deformations of $n$-BiHom-Lie algebras. https://arxiv.org/abs/2011.05560

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