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

2020/10/21 by Laraiedh, Ismail
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2011.05560

Abstract

In this paper we define and discuss the representations of n-BiHom-Lie algebra. We also introduce T_θ-extensions and T_θ^∗-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_θ^∗-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

Related

• Representations of Bihom-Lie algebras
• The construction of 3-Bihom-Lie algebras
• Split extensions of BiHom-Lie algebras
• Constructions and T^∗-Extensions of 3-Bihom-Lie Superalgebras
• Extensions of (super) Lie algebras