Lie Super-bialgebra Structures on the Super-BMS<sub>3</sub> Algebra

Cheng, Xiaosheng; Sun, Jiancai; Yang, Huihui

doi:10.1142/s1005386719000324

Cited by 7 publications

(5 citation statements)

References 12 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%

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%

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

Borowiec,

Brocki,

Kowalski-Glikman

et al. 2020

Preprint

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show abstract

“…The super-BMS 3 algebra W in this article is the centerless case of that. By [21], we can deduce that every Lie super-bialgebra structure on W is a triangular coboundary Lie super-bialgebra.…”

Section: Quantization Of Wmentioning

confidence: 97%

“…Theorem 1 (see [21]). Every Lie super-bialgebra structure on W is a triangular coboundary Lie super-bialgebra.…”

Section: Quantization Of Wmentioning

confidence: 99%

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Quantization of the Super-BMS3 Algebra

Yang

Wang

2022

Advances in Mathematical Physics

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In this article, we study quantization of super-BM S 3 algebra W . We quantize W by the Drinfel’d twist quantization technique and obtain a class of noncommutative and noncocommutative Hopf superalgebras.

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

Section: Jhep02(2021)084mentioning

confidence: 99%

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

Borowiec

Brocki

Kowalski-Glikman

et al. 2021

J. High Energ. Phys.

View full text Add to dashboard Cite

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.

show abstract

Lie Super-bialgebra Structures on the Super-BMS₃ Algebra

Cited by 7 publications

References 12 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

Quantization of the Super-BMS3 Algebra

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

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Lie Super-bialgebra Structures on the Super-BMS3 Algebra

Cited by 7 publications

References 12 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

Quantization of the Super-BMS3 Algebra

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

Contact Info

Product

Resources

About

Lie Super-bialgebra Structures on the Super-BMS₃ Algebra