Deformations of classical Lie algebras with homogeneous root system in characteristic two. I

Chebochko, N. G.

doi:10.1070/sm2005v196n09abeh003647

Cited by 10 publications

(20 citation statements)

References 5 publications

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“…The second cohomology group H 2 (L, L) is found in [6]. It is proved that dim H 2 (L, L) = 20, the weights of H 2 (L, L) are conjugate with respect to the Weyl group with α 1 + α 3 + α 5 , any weight subspace H 2 µ (L, L) is onedimensional and having a basis cocycle…”

Section: Group H 2 (L L) and Tri-vectorsmentioning

confidence: 99%

“…At present there does not seem to exist any complete de-scription of deformations of classical Lie algebras of characteristic 2 and Lie algebras of their derivations. Spaces of local deformations of classical Lie algebras with a homogeneous root system are found in [6]. Among the Lie algebras of series A, only the algebras Ā3 , Ā5 have nontrivial local deformations.…”

Section: Introductionmentioning

confidence: 99%

“…5,6). Therefore, ψ(ψ(x, y), z) = 0, ψ extends to global deformation and [ , ] + tψ defines the Lie multiplication.…”

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confidence: 99%

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Global deformations of a Lie algebra of type $\bar{A_5}$

Chebochko,

Kuznetsov

2019

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Section: Group H 2 (L L) and Tri-vectorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Global deformations of a Lie algebra of type $\bar{A_5}$

Chebochko,

Kuznetsov

2019

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“…Its deformation has been carried out in [7,21,22,31]. For p = 2, the situation is more complicated, see [6,10].…”

Section: Introductionmentioning

confidence: 99%

Cohomologically rigid solvable Lie superalgebras with model filiform and model nilpotent nilradical

Bouarroudj,

Navarro

2021

Preprint

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In this paper, we find a family SL n,m , in any arbitrary dimensions, of cohomologically rigid solvable Lie superalgebras with nilradical the model filiform Lie superalgebra L n,m . Moreover, we exhibit a family of cohomologically rigid solvable Lie superalgebras with nilradical the model nilpotent Lie superalgebra of generic characteristic sequence. Both cases correspond to solvable Lie superalgebras of maximal dimension for a given nilradical. Contrariwise, we will show that the family of Lie superalgebras SL n,m can be deformed if defined over a field of odd characteristic.

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“…Note that in characteristic zero, the vanishing of H 2 (g, g) for g simple follows from a classical result, known as second Whitehead's Lemma (see for example [HS97]). Interestingly, some of the classical simple Lie algebras admit non-trivial deformations in characteristic p = 2 or 3 (see [DZU76], [CK00], [CKK00], [CHE05]). …”

Section: ])mentioning

confidence: 99%