On 10 dimensional Exceptional Drinfel'd Algebras

TL;DR

This paper classifies ten-dimensional Exceptional Drinfeld algebras based on a specific restriction, revealing dualities and connections between different algebraic structures and string theory backgrounds.

Contribution

It provides a new classification of 10D EDA's with a focus on dualities and their implications for string theory backgrounds.

Findings

Classified 10D EDA's based on geometric subalgebra restrictions.

Identified dualities including a Nambu-Lie U-duality relating two Type IIA backgrounds.

Discovered that some algebras are related by different types of dualities, expanding understanding of algebraic structures in string theory.

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.