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LOCAL DERIVATIONS OF SOME JORDON ALGEBRAS OF DIMENSION WITH NILPOTENT ELEMENTS

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ARTICLE ANNOTATION

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In this paper, we study the general properties of derivations and local derivations of some Jordan algebras of dimension less than or equal to 4 with nilpotent elements. We obtain a necessary and sufficient condition for a linear mapping to be a derivation. Moreover, we prove that any local derivation of the considered Jordan algebras is a derivation.

AUTHORS

F.Arziqulov

O’zRFA matematika instituti Namangan bo’limi

N.Umrzaqov

Andijon davlat universiteti

Tags

# derivation# дифференцирование# Yordan algebrasi# chiziqli akslantirish# differensiallash# lokal differensiallash# Йорданова алгебра# линейное отображение# локальное дифференцирование# Jordon algebra# linear map# local derivation

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References

Ayupov Sh.A., Arzikulov F.N. Umrzaqov N.M. Local derivations on associative and Jordan matrix algebras. Uzbek Mathematical Journal, 2019, No 4, 99 24-38.

Ayupov Sh.A., Kudaybergenov K.K. Local derivations on finite-dimensional Lie algebras. Linear Algebra and its Applications 493, 381-398, 2016.

Iryna Kashuba, Maria Eugenia Martin. Deformations of Jordan algebras of dimension four. Journal of Algebra, Vol. 399, (2014) 277-289 p.