2020/09/09 by Yuho Sakatani, Sakatani, Yuho · 5 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2009.04454
openalex publication_date 2020/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Drinfel'd algebra gives the systematic construction of generalized parallelizable spaces and this allows us to study an extended T-duality, known as the Poisson-Lie T-duality. Recently, in order to find a generalized U-duality, an extended Drinfel'd algebra (ExDA), called the Exceptional Drinfel'd algebra (EDA) was proposed and a natural extension of the usual U-duality was studied both in the context of supergravity and membrane theory. In this paper, we clarify the general structure of ExDAs and show that an ExDA always gives a generalized parallelizable space, which may be regarded as a group manifold with generalized Nambu-Lie structures. We also discuss generalized Yang-Baxter deformations that are based on coboundary ExDAs. As important examples, we consider the En(n) EDA for n≤ 8 and study various aspects, both in terms of M-theory and type IIB theory.