Classification of three-dimensional solvable p-adic Leibniz algebras

On Isomorphism Classes of Low Dimensional Non-Lie Filiform Leibniz Algebras over Z_p

“…Besides the classification of algebras over complex field, there are also classifications over a special field which is p-adic (has zero characteristic). The classifications of filiform Leibniz algebras over p-adic have been done for the dimension up to eight (Ayupov and Kurbanbaev, 2010;Ladra et al, 2013;Khudoyberdiyev et al, 2010). Other than that Rakhimov et al, (2018) classified three dimensional Leibniz algebras over arbitrary field where = ℝ, ℤ 3 , ℤ 5 and ℤ 7 .…”

Classification of p-adic 6-dimensional filiform Leibniz algebras by solutions of x q = a

“…The field we are considering, Q , has zero characteristic. A number of results devoted to -adic algebras can be found in [4,7,12,17,20].…”

“…The descriptions of 3-dimensional solvable -adic Leibniz algebras [17] and 4-dimensional -adic filiform Leibniz algebras [4] show that already in these cases the lists of Leibniz algebras are essentially wider than in the complex case. Moreover, the classification of 5-dimensional -adic filiform Leibniz algebras is known.…”

On the solutions of the equation x^3+ax=b in Z*_3 with coefficients from Q_3

“…In similar complex case, the problem of classification in p-adic case is reduced to the solution of the equations in the field. The classifications of Leibniz algebras over the field of p-adic numbers have been obtained in [3], [9], [11].…”