On 10 dimensional Exceptional Drinfel'd Algebras

Abstract

Based on Mubarakzyanov's classification of four-dimensional real Lie algebras, we classify ten-dimensional Exceptional Drinfeld algebras (EDA). The classification is restricted to EDA's whose maximal isotropic (geometric) subalgebras cannot be represented as a product of a 3D Lie algebra and a 1D abelian factor. We collect the obtained algebras into families depending on the dualities found between them. Despite algebras related by a generalized Yang-Baxter deformation we find two algebras related by a different Nambu-Lie U-duality transformation. We show that this duality relates two Type IIA backgrounds.