Cohomology of $${\mathfrak{osp}}(1|2)$$ Acting on Linear Differential Operators on the Supercircle S 1|1

Basdouri, Imed; Ammar, Mabrouk Ben

doi:10.1007/s11005-007-0181-z

Cited by 23 publications

(17 citation statements)

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“…where the coefficients α j are constant. Then the map ∂b : Vect(S 1 ) × Vect(S 1 ) → P is given by ∂b(X, Y )(f ) = α 6 (2(f g (6) − f (6) g ) − 9(f (2) g (5) − f (5) g (2) ) + 5(f (3) g (4) − f (4) )g (3) ))ξ −3 5α 5 (f (2) g (4) − f (4) )g (2) )ξ −4 . (4.7)…”

Section: Second-order Integrability Conditionsmentioning

confidence: 99%

Deforming 𝔥-trivial the Lie algebra Vect(S¹) inside the Lie algebra of pseudodifferential operators Ψ𝒟𝒪

Basdouri

Bartouli

Lerbet

2017

Int. J. Geom. Methods Mod. Phys.

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In this paper, we consider the action of Vect(S1) by Lie derivative on the spaces of pseudodifferential operators [Formula: see text]. We study the [Formula: see text]-trivial deformations of the standard embedding of the Lie algebra Vect(S1) of smooth vector fields on the circle, into the Lie algebra of functions on the cotangent bundle [Formula: see text]. We classify the deformations of this action that become trivial once restricted to [Formula: see text], where [Formula: see text] or [Formula: see text]. Necessary and sufficient conditions for integrability of infinitesimal deformations are given.

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Section: Second-order Integrability Conditionsmentioning

confidence: 99%

Deforming 𝔥-trivial the Lie algebra Vect(S¹) inside the Lie algebra of pseudodifferential operators Ψ𝒟𝒪

Basdouri

Bartouli

Lerbet

2017

Int. J. Geom. Methods Mod. Phys.

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“…Ясно, что Υ является кограницей тогда и только тогда, когда̂︀ Υ является кограницей. Напомним, что пространство H 1 diff (osp(1|2), D 1 , ), которое было вычислено в [1], имеет вид…”

Section: определения и обозначенияunclassified

“…В этом подразделе мы вычислим пространство H 1 diff (osp(2|2), osp(1|2); D 2 , ) и докажем, что оно нетривиально в отличие от случая = 1, в котором H 1 diff (osp(1|2), sl(2); D 1 , ) = 0 (см. [1]). Отметим, что первый автор доказал в [11], что пространство H 1 diff ( (2), (1); D 2 , ) тоже нетривиально, тогда как, согласно [12], пространство H 1 diff ( (1), Vect(R); D 1 , ) тривиально.…”

Section: определения и обозначенияunclassified

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Когомологии алгебры $\mathfrak {osp}(2|2)$, действующей на пространствах линейных дифференциальных операторов на суперпространстве $\mathbb{R}^{1|2}$

Фраж¹,

Fraj²,

Бужельбен³

et al. 2012

Mat. Zametki

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“…, Υ λ,λ+ 5 2 ]] 9 2 ,λ+ 13 2 , J −1,λ 11 2 ]], , 4,λ = − (2λ + 9)(2λ + 3)(2λ 2 + 7λ + 2) (2λ + 7)(2λ + 1)(2λ 2 + 13λ + 17)…”

mentioning

confidence: 99%

Cohomology of the Lie Superalgebra of Contact Vector Fields on 𝕂^1|1 and Deformations of the Superspace of Symbols

Basdouri¹,

Ammar²,

Fraj³

et al. 2021

JNMP

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Following Feigin and Fuchs, we compute the first cohomology of the Lie superalgebra K(1) of contact vector fields on the (1,1)-dimensional real or complex superspace with coefficients in the superspace of linear differential operators acting on the superspaces of weighted densities. We also compute the same, but osp(1|2)-relative, cohomology. We explicitly give 1-cocycles spanning these cohomology. We classify generic formal osp(1|2)-trivial deformations of the K(1)-module structure on the superspaces of symbols of differential operators. We prove that any generic formal osp(1|2)-trivial deformation of this K(1)-module is equivalent to a polynomial one of degree ≤ 4. This work is the simplest superization of a result by Bouarroudj [On sl (2)

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Cohomology of $${\mathfrak{osp}}(1|2)$$ Acting on Linear Differential Operators on the Supercircle S 1|1

Cited by 23 publications

References 2 publications

Deforming 𝔥-trivial the Lie algebra Vect(S¹) inside the Lie algebra of pseudodifferential operators Ψ𝒟𝒪

Deforming 𝔥-trivial the Lie algebra Vect(S¹) inside the Lie algebra of pseudodifferential operators Ψ𝒟𝒪

Когомологии алгебры $\mathfrak {osp}(2|2)$, действующей на пространствах линейных дифференциальных операторов на суперпространстве $\mathbb{R}^{1|2}$

Cohomology of the Lie Superalgebra of Contact Vector Fields on 𝕂^1|1 and Deformations of the Superspace of Symbols

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Cohomology of $${\mathfrak{osp}}(1|2)$$ Acting on Linear Differential Operators on the Supercircle S 1|1

Cited by 23 publications

References 2 publications

Deforming 𝔥-trivial the Lie algebra Vect(S1) inside the Lie algebra of pseudodifferential operators Ψ𝒟𝒪

Deforming 𝔥-trivial the Lie algebra Vect(S1) inside the Lie algebra of pseudodifferential operators Ψ𝒟𝒪

Когомологии алгебры $\mathfrak {osp}(2|2)$, действующей на пространствах линейных дифференциальных операторов на суперпространстве $\mathbb{R}^{1|2}$

Cohomology of the Lie Superalgebra of Contact Vector Fields on 𝕂1|1 and Deformations of the Superspace of Symbols

Contact Info

Product

Resources

About

Deforming 𝔥-trivial the Lie algebra Vect(S¹) inside the Lie algebra of pseudodifferential operators Ψ𝒟𝒪

Deforming 𝔥-trivial the Lie algebra Vect(S¹) inside the Lie algebra of pseudodifferential operators Ψ𝒟𝒪

Cohomology of the Lie Superalgebra of Contact Vector Fields on 𝕂^1|1 and Deformations of the Superspace of Symbols