Deformations of the three-dimensional Lie algebra sl(2)

Show simple item record Ibrayeva, A.A. Ibraev, Sh.Sh. Turbayev, B.E. 2020-04-19T07:38:08Z 2020-04-19T07:38:08Z 2020-01-30
dc.identifier.citation Ibrayeva A.A. Deformations of the three-dimensional Lie algebra sl(2)/A.A. Ibrayeva, Sh.Sh. Ibraev, B.E. Turbayev//Қарағанды универисетінің хабаршысы. Математика Сериясы.=Вестник Карагандинского университета. Серия Математика.=Bulletin of the Karaganda University. Mathematics Series.-2020.-№1(97).-P. 44-51. ru_RU
dc.identifier.issn 2663-4872
dc.description.abstract Deformation is one of key questions of the structural theory of algebras over a field. Especially, it plays a important role in the classification of such algebras. In odd characteristics of algebraically closed fields, local deformations of classical Lie algebras are completely described. Local deformations are also known for classical Lie algebras with a homogeneous root system over an algebraically closed field of characteristic 2; except for the three-dimensional Lie algebra sl(2): In the characteristic 2; deformations of Lie algebras with an non-homogeneous root system are calculated only for Lie algebras of small ranks. In this paper we investigate deformations of the three-dimensional classical Lie algebra sl(2) over an algebraically closed field k of characteristic p = 2: We also describe three-dimensional two-sided Alia algebras associated with Lie algebra sl(2) in the characteristics 2 and 3: It is proved that, in characteristic 2, the space of local deformations of the Lie algebra sl(2) is five-dimensional. The structural specialty of the second cohomology space of the adjoint representation of the Lie algebra sl(2) are analyzed. In particular, the subspace of cosets of restricted cocycles is described. It is proved that the subspace of classes of restricted cocycles is two-dimensional and the corresponding local deformations are restricted Lie algebras in the sense of Jacobson. It was found that a family of simple three-dimensional unrestricted Lie algebras correspond to unrestricted non-trivial cocycles. In characteristics 2 and 3, three-dimensional two-sided Alia algebras that are non-isomorphic to the Lie algebra sl(2) are constructed. In the process of the study, a complete description of the space of all derivations of the Lie algebra sl(2) is obtained. ru_RU
dc.language.iso en ru_RU
dc.publisher KSU publ. ru_RU
dc.relation.ispartofseries Mathematics Series;№1(97)
dc.subject Lie algebra ru_RU
dc.subject module ru_RU
dc.subject representation ru_RU
dc.subject derivation ru_RU
dc.subject outer derivation ru_RU
dc.title Deformations of the three-dimensional Lie algebra sl(2) ru_RU
dc.type Article ru_RU

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