Extended Drinfel'd algebras and non-Abelian duality

Abstract

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 $E_{n(n)}$ EDA for $n\le 8$ and study various aspects, both in terms of M-theory and type IIB theory.

60 pages

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• Double Field Theory
• Exceptional Field Theory III: E${}_{8(8)}$
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• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• The E_{11} origin of all maximal supergravities
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Cited by in corpus (3)

• Poisson-Lie T-plurality for WZW backgrounds
• Extended Field Theories as higher Kaluza-Klein theories
• Half-maximal Extended Drinfel'd Algebras