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Left-right noncommutative Poisson algebras

José Casas;  Tamar Datuashvili;  Manuel Ladra — 2014

Open Mathematics

The notions of left-right noncommutative Poisson algebra (NPlr-algebra) and left-right algebra with bracket AWBlr are introduced. These algebras are special cases of NLP-algebras and algebras with bracket AWB, respectively, studied earlier. An NPlr-algebra is a noncommutative analogue of the classical Poisson algebra. Properties of these new algebras are studied. In the categories AWBlr and NPlr-algebras the notions of actions, representations, centers, actors and crossed modules are described as...

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

Manuel Ladra;  Bakhrom Omirov;  Utkir Rozikov — 2013

Open Mathematics

We study the p-adic equation x q = a over the field of p-adic numbers. We construct an algorithm which gives a solvability criteria in the case of q = p m and present a computer program to compute the criteria for any fixed value of m ≤ p − 1. Moreover, using this solvability criteria for q = 2; 3; 4; 5; 6, we classify p-adic 6-dimensional filiform Leibniz algebras.

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