Dual Lie Bialgebra Structures of W-algebra W(2, 2) Type

Song, Guang Ai; Su, Yu Cai; Yue, Xiao Qing

doi:10.1007/s10114-019-8287-7

Cited by 3 publications

(6 citation statements)

References 22 publications

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“…Therefore, several facts concerning W(2, 2) algebra are already established (see e.g. [33], [42] - [48]):…”

Section: Discussionmentioning

confidence: 99%

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BMS algebras in 4 and 3 dimensions, their quantum deformations and duals

Borowiec,

Brocki,

Kowalski-Glikman

et al. 2020

Preprint

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BMS symmetry is a symmetry of asymptotically flat spacetimes in vicinity of the null boundary of spacetime and it is expected to play a fundamental role in physics. It is interesting therefore to investigate the structures and properties of quantum deformations of these symmetries, which are expected to shed some light on symmetries of quantum spacetime. In this paper we discuss the structure of the algebra of extended BMS symmetries in 3 and 4 spacetime dimensions, realizing that these algebras contain an infinite number of distinct Poincaré subalgebras. Then we use these subalgebras to construct an infinite number of different Hopf algebras being quantum deformations of the BMS algebras. We also discuss different types of twist-deformations and the dual Hopf algebras, which could be interpreted as noncommutative, extended quantum spacetimes.

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“…Therefore, several facts concerning W(2, 2) algebra are already established (see e.g. [33], [42] - [48]):…”

Section: Discussionmentioning

confidence: 99%

“…For the sake of simplicity, following[33], we are using a pseudo-basis ζ m , χ k ; m, k ∈ Z in B 3 * instead of true basis ζ a,i , χ b,j in B 3• (see Appendix B ).…”

mentioning

confidence: 99%

BMS algebras in 4 and 3 dimensions, their quantum deformations and duals

Borowiec,

Brocki,

Kowalski-Glikman

et al. 2020

Preprint

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“…Comparing with the 3d Poincaré algebra in lightcone coordinates 1 35) if one identifies η +− = η −+ = −η 11 = n. In the formula above we rescaled the metric instead of using the embedding with rescaled generators, because the rescaling of l 0 changes the algebra (2.30) to which we embed. Note that, just as in the 4d case, these isomorphic embeddings are not automorphisms, since the metric components depend on n. 2 They are not compatible with automorphisms of the full B 3 algebra as explained in appendix A.…”

Section: D Gravitymentioning

confidence: 99%

“…Therefore, several facts concerning W(2, 2) algebra are already established (see e.g. [35], [44]- [50]):…”

Section: Jhep02(2021)084mentioning

confidence: 99%

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BMS algebras in 4 and 3 dimensions, their quantum deformations and duals

Borowiec

Brocki

Kowalski-Glikman

et al. 2021

J. High Energ. Phys.

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BMS symmetry is a symmetry of asymptotically flat spacetimes in vicinity of the null boundary of spacetime and it is expected to play a fundamental role in physics. It is interesting therefore to investigate the structures and properties of quantum deformations of these symmetries, which are expected to shed some light on symmetries of quantum spacetime. In this paper we discuss the structure of the algebra of extended BMS symmetries in 3 and 4 spacetime dimensions, realizing that these algebras contain an infinite number of distinct Poincaré subalgebras, a fact that has previously been noted in the 3 dimensional case only. Then we use these subalgebras to construct an infinite number of different Hopf algebras being quantum deformations of the BMS algebras. We also discuss different types of twist-deformations and the dual Hopf algebras, which could be interpreted as noncommutative, extended quantum spacetimes.

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Quantum Groups and Asymptotic Symmetries

Unger¹

2022

Preprint

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This thesis is devoted to the study of Lie bialgebra and Hopf algebra structures related to certain versions of non-commutative geometry constructed on infinite-dimensional Lie algebras that arise in the context of asymptotic symmetries of spacetime. We prove a number of theorems about cohomology groups that aid the classification of the Lie bialgebras and explicitly construct and analyze selected Hopf algebras. Particularly interesting behavior was found by studying the contraction limit of spacetimes with cosmological constant and the inclusion of central charges on the level of Lie bialgebras and Hopf algebras. Phenomenological consequences, like deformed in-vacuo dispersion relations, known from the study of κ-Poincaré quantum groups, are investigated. Furthermore, we examine how a new proposal in the context of the black hole information loss paradox and counterarguments against it are affected.

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Dual Lie Bialgebra Structures of W-algebra W(2, 2) Type

Cited by 3 publications

References 22 publications

BMS algebras in 4 and 3 dimensions, their quantum deformations and duals

BMS algebras in 4 and 3 dimensions, their quantum deformations and duals

BMS algebras in 4 and 3 dimensions, their quantum deformations and duals

Quantum Groups and Asymptotic Symmetries

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