The Automorphism Group Functor of the <i>N</i> = 4 Lie Conformal Superalgebra

Chang, Zhihua

doi:10.1080/00927872.2014.955577

Cited by 3 publications

(4 citation statements)

References 11 publications

(25 reference statements)

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“…From (14), (15), and (16), we deduce that H 1 ct ( Z, z G) = 0, i.e., the fiber of ρ over [1] also contains exactly one element.…”

Section: Classification Of Twisted Loop Conformal Superalgebrasmentioning

confidence: 93%

“…Next we consider the fiber of ρ over [1]. Twisting the Z-groups in (9) with respect to the cocycle z : Z → Aut D-conf (A D ), 1 → ω, we deduce that the fiber of ρ over [1] is measured by H 1 ct ( Z, z G). As Z-groups, z G = z G 1 × z G a ( D).…”

Section: Classification Of Twisted Loop Conformal Superalgebrasmentioning

confidence: 99%

“…Hence, χ(L ⊗ 1) ∈ B ⊆ A m is an eigenvector of (L ⊗ 1) (1) with eigenvalue 2. We can check that the eigenspace of (L ⊗ 1) (1)…”

Section: Classification Of Twisted Loop Conformal Superalgebrasmentioning

confidence: 99%

“…This work also provides a detail investigation of the automorphism group functors of the N = 1, 2, 3 conformal superalgebras. The structure of automorphism group functor of the small N = 4 conformal superalgebras has been explicitly determined in [1].…”

Section: Introductionmentioning

confidence: 99%

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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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“…From (14), (15), and (16), we deduce that H 1 ct ( Z, z G) = 0, i.e., the fiber of ρ over [1] also contains exactly one element.…”

Section: Classification Of Twisted Loop Conformal Superalgebrasmentioning

confidence: 93%

Section: Classification Of Twisted Loop Conformal Superalgebrasmentioning

confidence: 99%

“…Hence, χ(L ⊗ 1) ∈ B ⊆ A m is an eigenvector of (L ⊗ 1) (1) with eigenvalue 2. We can check that the eigenspace of (L ⊗ 1) (1)…”

Section: Classification Of Twisted Loop Conformal Superalgebrasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations