Semi‐simple Extension of the (Super) Poincaré Algebra

Soroka, D.; Soroka, Vyacheslav

doi:10.1155/2009/234147

Cited by 76 publications

(120 citation statements)

References 28 publications

Supporting

Mentioning

119

Contrasting

Order By: Relevance

“…The Maxwell algebra in d dimensions can be deformed to, depending on sign of the deformation parameter, so(d − 1, 2) ⊕ so(d − 1, 1) or so(d, 1) ⊕ so(d − 1, 1). The former is the direct sum of AdS d and d−dimensional Lorentz algebras and was found by Soroka and Soroka in [95] and subsequently studied in [96], while the latter is the direct sum of dS d and d−dimensional Lorentz algebras.…”

Section: Arbitrary Dimensionmentioning

confidence: 91%

See 1 more Smart Citation

On stabilization of Maxwell-BMS algebra

Concha

Safari

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

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.

show abstract

Section: Arbitrary Dimensionmentioning

confidence: 91%

“…The AdS-Lorentz symmetry has been studied in [67,77,95,102] and can be seen as a deformation of the Maxwell algebra. Further extensions of the AdS-Lorentz algebra in higher dimensions have been studied in [103][104][105] in order to recover the pure Lovelock theory.…”

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

confidence: 99%

On stabilization of Maxwell-BMS algebra

Concha

Safari

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…, where D = n + 2 is the dimension of space time, [34,25]. Conversely, it may be regarded as a Wigner-İnönü contraction [25] such that…”

Section: Deformations and Contractionsmentioning

confidence: 99%

Deforming the Maxwell-Sim algebra

2010

View full text Add to dashboard Cite

The Maxwell algebra is a non-central extension of the Poincaré algebra, in which the momentum generators no longer commute, but satisfy [P µ , P ν ] = Z µν . The charges Z µν commute with the momenta, and transform tensorially under the action of the angular momentum generators. If one constructs an action for a massive particle, invariant under these symmetries, one finds that it satisfies the equations of motion of a charged particle interacting with a constant electromagnetic field via the Lorentz force. In this paper, we explore the analogous constructions where one starts instead with the ISim subalgebra of Poincaré, this being the symmetry algebra of Very Special Relativity. It admits an analogous non-central extension, and we find that a particle action invariant under this Maxwell-Sim algebra again describes a particle subject to the ordinary Lorentz force. One can also deform the ISim algebra to DISim b , where b is a non-trivial dimensionless parameter. We find that the motion described by an action invariant under the corresponding MaxwellDISim algebra is that of a particle interacting via a Finslerian modification of the Lorentz force. In an appendix is it shown that the DISim b algebra is isomorphic to the extended Schrödinger algebra with b = 1 1−z .

show abstract

“…Recently the approach to the cosmological constant problem based on the tensor extension of the Poincaré algebra with the generators of the rotations M ab and translations P a [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] […”

mentioning

confidence: 99%

“…Here Z ab is a tensor generator, g ab is a constant Minkovski metric and c is some constant. In this paper we present another approach to the problem based on the gauge semisimple tensor extension of the D-dimensional Poincaré group which Lie algebra has the following form [13,21]:…”

mentioning

confidence: 99%