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

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.

Version for submission after referee's comments

References in corpus (2)

• Poisson-Lie U-duality in Exceptional Field Theory
• U-duality extension of Drinfel'd double

Cited by in corpus (1)

• E${}_{6(6)}$ Exceptional Drinfel'd Algebras