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## Classification of p-adic 6-dimensional filiform Leibniz algebras by solution of x^q=a

### Abstract

In this paper we study the $p$-adic equation $x^q=a$ over the field of $p$-adic numbers. We construct an algorithm of calculation of criteria of solvability in the case of $q=p^m$ and present a computer program to compute the criteria for fixed value of $m \leq p-1$. Moreover, using this solvability criteria for $q=2,3,4,5,6$, we classify $p$-adic 6-dimensional filiform Leibniz algebras.Comment: 15 page

Topics: Mathematics - Rings and Algebras, Mathematics - Number Theory, 11Sxx, 17A32
Year: 2011
OAI identifier: oai:arXiv.org:1103.5486