abstract

• Quadratic Hom-Lie algebras with equivariant twist maps are studied. They are completely characterized in terms of a maximal proper ideal that contains the kernel of the twist map and a complementary subspace to it that is either 1-dimensional, or has the structure of a simple Lie algebra. It is shown how the analogue of the double extension construction works well for quadratic Hom-Lie algebras with equivariant twist maps and prove that any indecomposable and quadratic Hom-Lie algebra with equivariant and nilpotent twist map can be identified with such a double extension.

authors

• García-Delgado R.
• Salgado González Gil
• Sánchez-Valenzuela O.A.

publication date

• 2023-01-01

published in

• arXiv  Journal

keywords

• Rings, algebras

Digital Object Identifier (DOI)

• 10.48550/arXiv.2304.06888

PubMed ID

start page

• 1

end page

• 21

volume

issue