Differential conformal superalgebras and their forms

Kač, Victor G.; Lau, Michael; Pianzola, Arturo

doi:10.1016/j.aim.2009.05.012

Cited by 9 publications

(47 citation statements)

References 15 publications

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“…The resulting differential conformal superalgebra structure over (C[t ±1 ], d dt ) allows us to understand L(A, σ) as a twisted form of L(A, id) with respect to theétale extension The above theory has been applied to the N = 1, 2, 3 and the small N = 4 conformal superalgebras. Concretely, the twisted loop conformal superalgebras corresponding to the N = 2 and small N = 4 superconformal algebras have been classified in [7]. The same classification for N = 3 has been obtained in [2].…”

Section: Introductionmentioning

confidence: 71%

On twisted large $N = 4$ conformal superalgebras

Chang

Pianzola

2013

Advances in Theoretical and Mathematical Physics

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We explicitly compute the automorphism group of the large N = 4 conformal superalgebra and classify the twisted loop conformal superalgebras based on the large N = 4 conformal superalgebra. By considering the corresponding superconformal Lie algebras, we validate the existence of only, two (up to isomorphism) such algebras as described in the physics literature. Our approach is based on viewing the objects to be classified as "étale twisted forms" of objects over the Laurent polynomial ring C[t ±1 ]. This allows methods from non-abelian cohomology (torsors) to enter into the picture. It is worth pointing out that the group of automorphisms of the large N = 4 conformal superalgebra is larger than the one described in the physics literature. Remarkably enough, both groups have the samé etale cohomology over C[t ±1 ] (which explains the agreement on the classification of the corresponding superconformal Lie algebras).e-print archive:

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Section: Introductionmentioning

confidence: 71%

On twisted large $N = 4$ conformal superalgebras

Chang

Pianzola

2013

Advances in Theoretical and Mathematical Physics

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“…which is the result of Proposition 3.69 in [10]. Downloaded by [Emory University] at 07:29 04 August 2015…”

Section: Corollary 43 Letmentioning

confidence: 80%

“…Thus r iM i = 0 i = 1 2 3 since R is an integral domain, i.e., T i ∈ ⊗ k R. Since Cur 2 k , by Corollary 3.17 in [10],…”

Section: The Group Functor Autmentioning

confidence: 88%

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The Automorphism Group Functor of the N = 4 Lie Conformal Superalgebra

Chang

2015

Communications in Algebra

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Differentials for Lie algebras

Kuttler

Pianzola

2015

Algebr Represent Theor

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Differential conformal superalgebras and their forms

Cited by 9 publications

References 15 publications

On twisted large $N = 4$ conformal superalgebras

On twisted large $N = 4$ conformal superalgebras

The Automorphism Group Functor of the N = 4 Lie Conformal Superalgebra

Differentials for Lie algebras

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