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Local And 2-Local Derivations Of Solvable Leibniz Algebras With Null-Filiform Nilradical, Sardorbek Umrzaqov
Local And 2-Local Derivations Of Solvable Leibniz Algebras With Null-Filiform Nilradical, Sardorbek Umrzaqov
Scientific Bulletin. Physical and Mathematical Research
In the works of Ayupov, Khudoyberdiyev and Yusupov proved that the local and 2-local derivation of solvable Leibniz algebras with model nilradical are derivations. Solvable Leibniz algebras with null-filiform nilradical are the partial case of solvable Leibniz algebras with model nilradical. However, the proof in the paper is different from model nilradical case. The derivation is a fundamental notion in mathematics. Derivations play a prominent role in algebra. There are many generalizations of derivations as antiderivation, δ-derivations, ternary derivations and (α,β,γ)-derivations. One of the important generalizations of derivation is local and 2-local derivations. Local derivations defined by Kadison, Larson and …
Local And 2-Local Derivation On Solvable Leibniz Algebras Whose Nilradical Is A Quasi-Filiform Leibniz Algebra Of Maximum Length, Shavkat Ayupov, Bakhtiyor Yusupov
Local And 2-Local Derivation On Solvable Leibniz Algebras Whose Nilradical Is A Quasi-Filiform Leibniz Algebra Of Maximum Length, Shavkat Ayupov, Bakhtiyor Yusupov
Karakalpak Scientific Journal
We show that any local derivation on the solvable Leibniz algebras whose nilradical is a quasi-filiform Leibniz algebra of maximum length with the maximal dimension of complementary space to the nilradical is a derivation. Moreover, a similar problem concerning 2-local derivations of such algebras is investigated.