Double Extensions of Multiplicative Restricted Hom-Lie Algebras

2023/11/17 by Mao, Dan, Hao, Zeyu, Chen, Liangyun
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2401.08592

Abstract

In this paper, we study the double extension of a restricted quadratic Hom-Lie algebra (V,[⋅,⋅]_V,α_V,B_V), which is an enlargement of V by means of a central extension and a restricted derivation \mathscrD. In particular, we prove that the double extension of a restricted quadratic Hom-Lie algebra V with a \mathscrD-invariant bilinear form B_V is restricted. Conversely, any irreducible restricted quadratic Hom-Lie algebra with nonzero center is proved to be the double extension of another restricted quadratic Hom-Lie algebra.

Related

• Hom-Lie Algebras with Symmetric Invariant NonDegenerate Bilinear Forms
• Double extensions of restricted Lie (super)algebras
• Double extensions for quadratic Hom-Lie algebras with equivariant twist maps
• Modular structure theory on Hom-Lie algebras
• Inductive description of quadratic Hom-Lie algebras with twist maps in the centroid