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- W4301479812 abstract "The aim of this paper is to introduce and study quadratic Hom-Lie algebras, which are Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms. We provide several constructions leading to examples and extend the double extension theory to Hom-Lie algebras. We reduce the case where the twist map is invertible to the study of involutive quadratic Lie algebras. We establish a correspondence between the class of involutive quadratic Hom-Lie algebras and quadratic simple Lie algebras with symmetric involution. Centerless involutive quadratic Hom-Lie algebras are characterized. Also elements of a representation theory for Hom-Lie algebras, including adjoint and coadjoint representations are supplied with application to quadratic Hom-Lie algebras." @default.
- W4301479812 created "2022-10-05" @default.
- W4301479812 creator A5003635606 @default.
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- W4301479812 date "2010-09-21" @default.
- W4301479812 modified "2023-10-16" @default.
- W4301479812 title "Hom-Lie Algebras with Symmetric Invariant NonDegenerate Bilinear Forms" @default.
- W4301479812 doi "https://doi.org/10.48550/arxiv.1009.4226" @default.
- W4301479812 hasPublicationYear "2010" @default.
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