The automorphism group of Poisson algebras on k [x, y]

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dc.contributor.author Turusbekova, U.
dc.contributor.author Azieva, G.
dc.date.accessioned 2018-04-17T09:45:11Z
dc.date.available 2018-04-17T09:45:11Z
dc.date.issued 2017-09-29
dc.identifier.citation Turusbekova U. The automorphism group of Poisson algebras on k [x, y]/U. Turusbekova, G. Azieva//Қарағанды универисетінің хабаршысы. МАТЕМАТИКА Сериясы.=Вестник Карагандинского университета. Серия МАТЕМАТИКА.=Bulletin of the Karaganda University. MATHEMATICS Series.-2017. №3.Р.117-124. ru_RU
dc.identifier.uri http://rep.ksu.kz/handle/data/2596
dc.description.abstract Poisson algebras play a key role in the Hamiltonian mechanics, symplectic geometry and also are central in the study of quantum groups. At present, Poisson algebras are investigated by the many mathematicians of Russia, France, the USA, Brazil, Argentina, Bulgaria etc. The purpose of the present paper is to describe the automorphism groups of polynomial algebras endowed with additional structure, namely, with Poisson brackets. For any f ∈ k [x, y] one can transform associative-commutative algebra k [x, y] into a Poisson algebra Pf by defining a Poisson bracket by the rule {x, y} = f . Obviously, a structure of the automorphism group Gf of Poisson algebra Pf depends on the element f . A complete description of group Gf is given for the polynomial f of rank less or equals to 1. In present paper all algebras are considered over any field k of characteristic 0. ru_RU
dc.language.iso en ru_RU
dc.publisher KSU Publ. ru_RU
dc.relation.ispartofseries Қарағанды универисетінің хабаршысы. МАТЕМАТИКА Сериясы.=Вестник Карагандинского университета. Серия МАТЕМАТИКА.=Bulletin of the Karaganda University. MATHEMATICS Series.;№ 3(87)/2017
dc.subject Poisson algebras ru_RU
dc.subject polynomial algebras ru_RU
dc.subject automorphisms ru_RU
dc.subject additional structure ru_RU
dc.title The automorphism group of Poisson algebras on k [x, y] ru_RU
dc.title.alternative k[x, y] кeпмyшелiктер алгебрасындағы Пуассон алгебраларының автоморфизмдер тобы ru_RU
dc.title.alternative Группа автоморфизмов алгебры Пуассона на k[x, y] ru_RU
dc.type Article ru_RU


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