Classification of three-dimensional solvable \(p\)-adic Leibniz algebras
type: Item
instance of: scholarly article
title: Classification of three-dimensional solvable \(p\)-adic Leibniz algebras
zbMATH Open document ID: 1305.17002
DOI: 10.1134/S2070046610030039
author: A. Kh. Khudoyberdiyev
author: T. K. Kurbanbaev
author: B. A. Omirov
published in: \(p\)-Adic Numbers, Ultrametric Analysis, and Applications
publication date: 2012-11-13T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 17A32
zbMATH DE Number: 6105045
zbMATH Keywords: Leibniz algebra
zbMATH Keywords: Lie algebra
zbMATH Keywords: classification
zbMATH Keywords: p-adic field
Wikidata QID: Q123277675
reviewed by: I. S. Rakhimov
MaRDI profile type: Publication
cites work: Q5425786
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description: scientific article; zbMATH DE number 6105045