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Local and 2-local derivations of solvable Leibniz algebras

V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 81, Mirzo Ulughbek Street, Tashkent 100170, Uzbekistan

National University of Uzbekistan, 4, University Street, Tashkent 100174, Uzbekistan

E-mail Address: sh_ayupov@mail.ru

E-mail Address: shavkat.ayupov@mathinst.uz

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Abror Khudoyberdiyev

V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 81, Mirzo Ulughbek Street, Tashkent 100170, Uzbekistan

National University of Uzbekistan, 4, University Street, Tashkent 100174, Uzbekistan

E-mail Address: khabror@mail.ru

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Bakhtiyor Yusupov

National University of Uzbekistan, 4, University Street, Tashkent 100174, Uzbekistan

E-mail Address: baxtiyor_yusupov_93@mail.ru

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https://doi.org/10.1142/S021819672050037XCited by:12 (Source: Crossref)

Abstract

We show that any local derivation on the solvable Leibniz algebras with model or abelian nilradicals, whose dimension of complementary space is maximal is a derivation. We show that solvable Leibniz algebras with abelian nilradicals, which have $1$ dimension complementary space, admit local derivations which are not derivations. Moreover, similar problem concerning $2$ -local derivations of such algebras is investigated and an example of solvable Leibniz algebra is given such that any $2$ -local derivation on it is a derivation, but which admits local derivations which are not derivations.

Communicated by I. Shestakov

Keywords:

AMSC: 17A32, 17B30, 17B10

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