U-duality extension of Drinfel'd double

Abstract

A family of algebras ${\mathcal{E}}_n$ that extends the Lie algebra of the Drinfel'd double is proposed. This allows us to systematically construct the generalized frame fields $E_A{}^I$ which realize the proposed algebra by means of the generalized Lie derivative, i.e., ${\hat{\mathcal{L}}}_{E_A}{E}_B{}^I=-{\mathcal{F}}_{AB}{}^C{E}_C{}^I$. By construction, the generalized frame fields include a twist by a Nambu-Poisson tensor. A possible application to the non-Abelian extension of U-duality and a generalization of the Yang-Baxter deformation are also discussed.

34 pages; v2: references added, expanded the discussion of the Yang-Baxter deformation; v3: a reference added, typos corrected, to appear in PTEP; v4: footnotes 5 and 8 added, a redundant condition in Eq.(6.20) removed

References in corpus (16)

• Double Field Theory
• Generalized Geometry and M theory
• Exceptional Field Theory III: E${}_{8(8)}$
• Gauged Double Field Theory
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• The E_{11} origin of all maximal supergravities
• Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
• Doubled aspects of generalised dualities and integrable deformations
• Double Field Theory on Group Manifolds
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Tri-vector deformations in $d=11$ supergravity
• Non-Abelian T-duality as a Transformation in Double Field Theory
• Doubled Aspects of Vaisman Algebroid and Gauge Symmetry in Double Field Theory
• E(7(7)) and d=11 supergravity
• Fluxes in Exceptional Field Theory and Threebrane Sigma-Models

Cited by in corpus (34)

• The Geometry, Branes and Applications of Exceptional Field Theory
• Poisson-Lie U-duality in Exceptional Field Theory
• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Non-Abelian U-duality for membrane
• Non-abelian tri-vector deformations in d=11 supergravity
• Exploring Exceptional Drinfeld Geometries
• Polyvector deformations in eleven-dimensional supergravity
• G-algebroids: a unified framework for exceptional and generalised geometry, and Poisson-Lie duality
• Non-abelian U-duality at work
• On non-abelian U-duality of 11D backgrounds
• Consistent Truncations and Dualities
• Exceptional algebroids and type IIB superstrings
• Global Aspects of Doubled Geometry and Pre-rackoid
• All maximal gauged supergravities with uplift
• Currents, charges and algebras in exceptional generalised geometry
• Generalized Dualities and Supergroups
• More on Doubled Aspects of Algebroids in Double Field Theory
• Generalizing eleven-dimensional supergravity
• Jacobi-Lie T-plurality
• Tri-vector deformations on compact isometries
• Generalised U-dual solutions via ISO(7) gauged supergravity
• On 10 dimensional Exceptional Drinfel'd Algebras
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Extended Drinfel'd algebras and non-Abelian duality
• Integrability structures in string theory
• Y-algebroids and $E_{7(7)}\times {\mathbb{R}}^{+}$-generalised geometry
• Poisson-Lie T-plurality for dressing cosets
• Jacobi-Lie Models and Supergravity Equations
• Poisson-Lie T-plurality for WZW backgrounds
• T-folds as Poisson-Lie plurals
• Classification of six-dimensional Leibniz algebras ${\mathcal E}_3
• Non-isometric U-dualities
• Half-maximal Extended Drinfel'd Algebras
• Extended Field Theories as higher Kaluza-Klein theories