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arXiv · 2003.06164

Classification of six-dimensional Leibniz algebras ${\mathcal E}_3

Ladislav Hlavaty
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Abstract

Leibniz algebras ${\mathcal E}_n$ were introduced as algebraic structure underlying U-duality. Algebras ${\mathcal E}_3$ derived from Bianchi three-dimensional Lie algebras are classified here. Two types of algebras are obtained: Six-dimensional Lie algebras that can be considered extension of semi-Abelian four-dimensional Drinfeld double and unique extensions of non-Abelian Bianchi algebras. For all of the algebras explicit forms of generalized frame fields are given.

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Ladislav Hlavaty. 2020-03-13. Classification of six-dimensional Leibniz algebras ${\mathcal E}_3. https://doi.org/10.1093/ptep/ptaa082

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