Classification of three-dimensional solvable \(p\)-adic Leibniz algebras
In the paper the authors classify three-dimensional Leibniz algebras over p-adic numbers. In Section 3 the list of three-dimensional solvable Lie algebras over p-adic numbers is given. Section 4 contains the list of all possible non-Lie Leibniz algebra structures on three-dimensional vector space over \(p\)-adic numbers. The method of classification is based on case by case consideration of few numerical isomorphism invariants and some simple properties of \(p\)-adic numbers. The invariants used in the paper are dimensions of right annihilator and degree of the algebra. Depending on the values of the invariants choosing a basis the authors construct tables of multiplications, then changing the basis they bring each table either to single algebra or to some parametric family of algebras.
scientific article; zbMATH DE number 6105045
scientific article