The low-dimensional algebraic cohomology of the Witt and the Virasoro algebra

Ecker, Jill Marie-Anne; Schlichenmaier, Martin

doi:10.1088/1742-6596/1194/1/012032

Cited by 11 publications

(9 citation statements)

References 39 publications

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“…To establish rigidity of vir L ⊕vir R , we show that H 2 (vir L ⊕vir R ; vir L ⊕ vir R ) = 0. To this end, as in the previous case, we use decomposition, The Hochschild-Serre spectral sequence associated to the above exact sequence with coefficients in vir L is convergent with the following property [80]: On the other hand, we know (see [19,20] for more detail)…”

Section: Formal Deformationsmentioning

confidence: 99%

On rigidity of 3d asymptotic symmetry algebras

Parsa

Safari

Sheikh-Jabbari

2019

J. High Energ. Phys.

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We study rigidity and stability of infinite dimensional algebras which are not subject to the Hochschild-Serre factorization theorem. In particular, we consider algebras appearing as asymptotic symmetries of three dimensional spacetimes, the bms 3 , u(1) Kac-Moody and Virasoro algebras. We construct and classify the family of algebras which appear as deformations of bms 3 , u(1) Kac-Moody and their central extensions by direct computations and also by cohomological analysis. The Virasoro algebra appears as a specific member in this family of rigid algebras; for this case stabilization procedure is inverse of the Inönü-Wigner contraction relating Virasoro to bms 3 algebra. We comment on the physical meaning of deformation and stabilization of these algebras and relevance of the family of rigid algebras we obtain.

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Section: Formal Deformationsmentioning

confidence: 99%

On rigidity of 3d asymptotic symmetry algebras

Parsa

Safari

Sheikh-Jabbari

2019

J. High Energ. Phys.

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“…At the infinite-dimensional level, the Hochschild-Serre factorization theorem does not apply. Then, the study of the stability of infinite dimensional algebras and asymptotic symmetries has been explored case-by-case [56][57][58][59][60]. It is then worth it to explore the stability of other known infinite dimensional algebras.…”

Section: Introduction and Motivationsmentioning

confidence: 99%

On stabilization of Maxwell-BMS algebra

Concha

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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“…We will also provide results for the general tensor densities modules. Some of the results proven here have been presented as preprints in 2017 and 2018 [5,6]. This document unites them and should replace them.…”

Section: Introductionmentioning

confidence: 82%

The low-dimensional algebraic cohomology of the Witt and the Virasoro algebra with values in natural modules

Ecker

Schlichenmaier

2021

Banach Center Publ.

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The main aim of this contribution is to compute the low-dimensional algebraic cohomology of the Witt and the Virasoro algebra with values in the adjoint and the trivial module. The last section includes results for the general tensor densities modules, presented without proof. One of our main results is that the third algebraic cohomology of the Witt algebra with values in the adjoint module vanishes, while it is one-dimensional for the Virasoro algebra. The first and the second algebraic cohomology of the Witt and the Virasoro algebra with values in tensor densities modules vanish for almost all modules. In the case they do not vanish, we give explicit expressions for the generating cocycles. In our work, we consider algebraic cohomology and not only the sub-complex of continuous cohomology, meaning we do not put any continuity constraints on the cochains. Consequently, our results are independent of any choice of an underlying topology, and valid for any concrete realizations of the considered Lie algebras.

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The low-dimensional algebraic cohomology of the Witt and the Virasoro algebra

Cited by 11 publications

References 39 publications

On rigidity of 3d asymptotic symmetry algebras

On rigidity of 3d asymptotic symmetry algebras

On stabilization of Maxwell-BMS algebra

The low-dimensional algebraic cohomology of the Witt and the Virasoro algebra with values in natural modules

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