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Computing Matrix Representations of Filiform Lie Algebras

  • Manuel Ceballos
  • Juan Núñez
  • Ángel F. Tenorio
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6244)

Abstract

In this paper, we compute minimal faithful unitriangular matrix representations of filiform Lie algebras. To do it, we use the nilpotent Lie algebra, \(\mathfrak{g}_n\), formed of n ×n strictly upper-triangular matrices. More concretely, we search the lowest natural number n such that the Lie algebra \(\mathfrak g_n\) contains a given filiform Lie algebra, also computing a representative of this algebra. All the computations in this paper have been done using MAPLE 9.5.

Keywords

Filiform Lie Algebra Minimal Faithful Unitriangular Matrix Representation Algorithm 

2000 Mathematics Subject Classification

17B30 68W40 68Q25 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Manuel Ceballos
    • 1
  • Juan Núñez
    • 1
  • Ángel F. Tenorio
    • 2
  1. 1.Departamento de Geometría y Topología, Facultad de MatemáticasUniversidad de SevillaSpain
  2. 2.Dpto. de Economía, Métodos Cuantitativos e Historia Económica, Escuela Politécnica SuperiorUniversidad Pablo de OlavideSevilleSpain

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