Automorphisms and twisted forms of the $N=1,2,3$ Lie conformal superalgebras

Chang, Zhihua; Pianzola, Arturo

doi:10.4310/cntp.2011.v5.n4.a1

Cited by 5 publications

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“…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]. This work also provides a detail investigation of the automorphism group functors of the N = 1, 2, 3 conformal superalgebras.…”

Section: Introductionmentioning

confidence: 63%

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: 63%

On twisted large $N = 4$ conformal superalgebras

Chang

Pianzola

2013

Advances in Theoretical and Mathematical Physics

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“…For the N = 1 2 3 Lie conformal superalgebras N , the particular choice that W = N has been considered in [1]. In this situation,…”

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confidence: 99%

“…In order to completely classify twisted loop conformal superalgebras based on one of the N = 2 and N = 4 conformal superalgebras , the automorphism group Aut has been determined in [10]. The automorphism group functors of the N = 1 2 3 conformal superalgebras were studied in [1] as well. Interestingly, for the N = 1 2 3 Lie conformal superalgebra N , Aut N has a subgroup functor GrAut N such that GrAut N = Aut N for = R with R an integral domain, and GrAut N is the group functor obtained by lifting the kgroup scheme O N of N × N -orthogonal matrices via the forgetful functor fgt k-drng → k-rng = R → R, i.e.,…”

Section: Introductionmentioning

confidence: 99%

“…In order to completely classify twisted loop conformal superalgebras based on one of the N = 2 and N = 4 conformal superalgebras A, the automorphism group Aut(A)( D) has been determined in [10]. The automorphism group functors of the N = 1, 2, 3 conformal superalgebras were studied in [1] as well. Interestingly, for the…”

Section: Introductionmentioning

confidence: 99%

“…It has been conjecture in [1] that the automorphism group functor Aut(F ) of the N = 4 Lie conformal superalgebra F also satisfies similar properties:…”

Section: Introductionmentioning

confidence: 99%

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

Chang

2015

Communications in Algebra

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Deformations and generalized derivations of Lie conformal superalgebras

Zhao

Chen

Yuan

2017

Journal of Mathematical Physics

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The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Lie conformal superalgebras. Firstly, we construct the semidirect product of a Lie conformal superalgebra and its conformal module, and study derivations of this semidirect product. Secondly, we develop cohomology theory of Lie conformal superalgebras and discuss some applications to the study of deformations of Lie conformal superalgebras. Finally, we introduce generalized derivations of Lie conformal superalgebras and study their properties.Comment: 26page

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Automorphisms and twisted forms of the $N=1,2,3$ Lie conformal superalgebras

Cited by 5 publications

References 0 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

Deformations and generalized derivations of Lie conformal superalgebras

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