U-duality extension of Drinfel'd double

Yuho Sakatani

doi:10.1093/ptep/ptz172

U-duality extension of Drinfel'd double

High Energy Physics - Theory 2020-04-27 v4 Differential Geometry Symplectic Geometry

Authors: Yuho Sakatani

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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.

Keywords

U-duality Drinfel'd double generalized frame fields Nambu-Poisson tensor Yang-Baxter deformation

Cite

@article{arxiv.1911.06320,
  title  = {U-duality extension of Drinfel'd double},
  author = {Yuho Sakatani},
  journal= {arXiv preprint arXiv:1911.06320},
  year   = {2020}
}

Comments

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

U-duality extension of Drinfel'd double

Abstract

Keywords

Cite

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