Poisson-Lie T-plurality

Unge, Rikard von

doi:10.1088/1126-6708/2002/07/014

Cited by 62 publications

(37 citation statements)

References 35 publications

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“…In particular, wheñ f ab c = 0 , it is called the non-Abelian T -duality. A general O(D, D) transformation is called the PL T -plurality transformation [60], but in this paper, we denote an arbitrary O(D, D) transformation as the PL T -duality.…”

Section: )mentioning

confidence: 99%

“…Here,£ V is the generalized Lie derivative in EFT, which generates the gauge transformations in EFT. The systematic construction of E A I is indispensable to perform the PL T -duality or its extension PL T -plurality [60], and we expect that the U -duality extension presented in this paper will be useful in studying the non-Abelian extension of U -duality.…”

Section: Introductionmentioning

confidence: 99%

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U -duality extension of Drinfel’d double

Sakatani

2020

Progress of Theoretical and Experimental Physics

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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., $\hat{\pounds}_{E_A}E_B{}^I =-\mathcal{F}_{AB}{}^C\,E_C{}^I$. 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.

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Section: )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

U -duality extension of Drinfel’d double

Sakatani

2020

Progress of Theoretical and Experimental Physics

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“…Using (26) with the condition sdetA = 0 and imposing the condition that A must be in the form (38), we obtain table 3 for automorphism supergroups 10 Note that the superalgebra A is a one dimensional abelian Lie superalgebras with one fermionic generator and superalgebra A 1,1 is its bosonization. …”

Section: A(amentioning

confidence: 99%

“…Using (26) with the condition sdetA = 0 and imposing the condition that A must be in the form (38), we obtain table 3 for automorphism supergroups. …”

Section: Two and Three Dimensional Lie Superalgebras And Their Automomentioning

confidence: 99%

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Classification of two and three dimensional Lie superbialgebras

Eghbali

Rezaei-Aghdam

Heidarpour

2010

Journal of Mathematical Physics

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AdS3×S3$AdS_3 \times S^3$ Background From Poisson–Lie T‐Duality

Eghbali

2024

Fortschritte der Physik

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The author proceed to construct a dual pair for the background by applying non‐Abelian T‐duality (here as Poisson–Lie [PL] T‐duality on a semi‐Abelian double). By using a certain parametrization of the 4‐dimensional Lie group and by a suitable choice of spectator‐dependent matrices the original ‐model including the metric and a non‐trivial ‐field are constructed. The dual background constructed by means of the PL T‐duality with the spectators is an asymptotically flat one with a potential black hole interpretation supported by a non‐trivial ‐flux whose metric contains the true singularity with a single horizon. The question of classical integrability of the non‐Abelian T‐dual ‐models under consideration is addressed, and their corresponding Lax pairs are found, depending on some spectral parameters. Finally, the conformal invariance conditions of the models are checked up to two‐loop order, and it has been concluded that the resulting model is indeed a solution of supergravity.

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Poisson-Lie T-plurality

Cited by 62 publications

References 35 publications

U -duality extension of Drinfel’d double

U -duality extension of Drinfel’d double

Classification of two and three dimensional Lie superbialgebras

AdS3×S3$AdS_3 \times S^3$ Background From Poisson–Lie T‐Duality

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