Low-Dimensional Cohomology Groups of the Lie Algebras W(<i>a</i>,<i>b</i>)

Gao, Shoulan; Jiang, Cuipo; Pei, Yufeng

doi:10.1080/00927871003591835

Cited by 45 publications

(49 citation statements)

References 19 publications

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“…For s = 1 the algebra (A.2) coincides with the standard (non-centrally extended) BMS 3 algebra [98,99], while for s = 0 the algebra (A.2) reduces to the one in [52]. For generic s, the algebra (A.2) is W (0, −s) [100,101] which may be obtained as algebraic deformation of BMS 3 [101].…”

Section: Comments and Further Developmentsmentioning

confidence: 99%

Spacetime Structure near Generic Horizons and Soft Hair

et al. 2020

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We explore the spacetime structure near non-extremal horizons in any spacetime dimension greater than two and discover a wealth of novel results: 1. Different boundary conditions are specified by a functional of the dynamical variables, describing inequivalent interactions at the horizon with a thermal bath. 2. The near horizon algebra of a set of boundary conditions, labeled by a parameter s, is given by the semi-direct sum of diffeomorphisms at the horizon with "spin-s supertranslations". For s = 1 we obtain the first explicit near horizon realization of the Bondi-Metzner-Sachs algebra. 3. For another choice, we find a non-linear extension of the Heisenberg algebra, generalizing recent results in three spacetime dimensions. This algebra allows to recover the aforementioned (linear) ones as composites. 4. These examples allow to equip not only black holes, but also cosmological horizons with soft hair. We also discuss implications of soft hair for black hole thermodynamics and entropy.

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Section: Comments and Further Developmentsmentioning

confidence: 99%

Spacetime Structure near Generic Horizons and Soft Hair

et al. 2020

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“…As mentioned before this algebra is known as the twisted Schrödinger-Virasoro algebra. According to the theorem 2.2 in [47] we know that there is no central term in the [J m , P n ] commutator. Let us note that since the three parametersᾱ,β andν are independent, there is no solution for the above expression forᾱ,β,ν = 0.…”

Section: Central Extension Of Deformed Max 3 Algebra In Its Ideal Partmentioning

confidence: 99%

On stabilization of Maxwell-BMS algebra

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Safari

2020

J. High Energ. Phys.

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In this work we present different infinite dimensional algebras which appear as deformations of the asymptotic symmetry of the three-dimensional Chern-Simons gravity for the Maxwell algebra. We study rigidity and stability of the infinite dimensional enhancement of the Maxwell algebra. In particular, we show that three copies of the Witt algebra and the bms 3 ⊕ witt algebra are obtained by deforming its ideal part. New family of infinite dimensional algebras are obtained by considering deformations of the other commutators which we have denoted as M(a, b; c, d) and M(ᾱ,β;ν). Interestingly, for the specific values a = c = d = 0, b = − 1 2 the obtained algebra M(0, − 1 2 ; 0, 0) corresponds to the twisted Schrödinger-Virasoro algebra. The central extensions of our results are also explored. The physical implications and relevance of the deformed algebras introduced here are discussed along the work.

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“…One may show, following analysis of [59], that W(a, b;ā,b) for generic values of the parameters admits two independent central extensions which may be associated with deforming the algebra by two independent unit elements added to the algebra. The centrally extended W-algebra which will be denoted by W(a, b;ā,b) is given by: As in the case of W (a, b) algebras discussed in [1,55], there may be special points in the (a, b,ā,b) parameter space which admit other central terms. As the first case let us consider bms 4 = W( −1 2 , −1 2 , −1 2 , −1 2 ).…”

Section: Deformations Of Special W Algebrasmentioning

confidence: 99%

“…Recalling that in the W (a, b) case there is a possibility of a central extension in L, T sector a = 0, b = 1 case[55], we examine if there is a possibility of central extension in [L m , T p,q ] or [L m , T p,q ] for specific values of a, b,ā,b parameters. Explicitly, consider[L m , T p,q ] = −(a + bm + p)T m+p,q + f (m, p)δ q,0 , (6.2)and[L n , T p,q ] = −(ā +bn + p)T p,n+q +f (n, q)δ p,0 , (6.3) where f (m, n) andf (m,n) are arbitrary functions.…”

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BMS4 algebra, its stability and deformations

Safari

Sheikh-Jabbari

2019

J. High Energ. Phys.

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We continue analysis of [1] and study rigidity and stability of the bms 4 algebra and its centrally extended version bms 4 . We construct and classify the family of algebras which appear as deformations of bms 4 and in general find the four-parameter family of algebras W(a, b;ā,b) as a result of the stabilization analysis, where bms 4 = W(−1/2, −1/2; −1/2, −1/2). We then study the W(a, b;ā,b) algebra, its maximal finite subgroups and stability for different values of the four parameters. We prove stability of the W(a, b;ā,b) family of algebras for generic values of the parameters. For special cases of (a, b) = (ā,b) = (0, 0) and (a, b) = (0, −1), (ā,b) = (0, 0) the algebra can be deformed. In particular we show that centrally extended W(0, −1; 0, 0) algebra can be deformed to an algebra which has three copies of Virasoro as a subalgebra. We briefly discuss these deformed algebras as asymptotic symmetry algebras and the physical meaning of the stabilization and implications of our result.

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Low-Dimensional Cohomology Groups of the Lie Algebras W(a,b)

Cited by 45 publications

References 19 publications

Spacetime Structure near Generic Horizons and Soft Hair

Spacetime Structure near Generic Horizons and Soft Hair

On stabilization of Maxwell-BMS algebra

BMS4 algebra, its stability and deformations

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