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A computational study of a family of nilpotent Lie algebras

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Abstract

This paper describes an algorithm to compute the law of the Lie algebra \(\mathfrak{g}_{n}\) associated with the Lie group G n , formed of all the n×n upper-unitriangular matrices. The goal of this paper is to show the algorithm that computes the law of \(\mathfrak{g}_{n}\) and its implementation using the symbolic computation package MAPLE. In addition, the complexity of the algorithm is described.

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References

  1. Beck RE, Kolman B (1973) Computers in Lie algebras I. Calculation of inner multiplicities. SIAM J Appl Math 25:300–312

    Article  MathSciNet  MATH  Google Scholar 

  2. Benjumea JC, Núñez J, Tenorio AF (2007) The maximal Abelian dimension of linear algebras formed by strictly upper triangular matrices. Theor Math Phys 152:1225–1233

    Article  MATH  Google Scholar 

  3. Benjumea JC, Núñez J, Tenorio AF (2008) Minimal linear representations of the low-dimensional nilpotent lie algebras. Math Scand 102:17–26

    MathSciNet  MATH  Google Scholar 

  4. de Graaf WA (2005) Classification of solvable Lie algebras. Exp Math 14:15–25

    Article  MATH  Google Scholar 

  5. Draisma J (2003) Constructing Lie algebras of first order differential operators. J Symb Comput 36:685–698

    Article  MathSciNet  MATH  Google Scholar 

  6. Fulton W, Harris J (1991) Representation theory: a first course. Springer, New York

    MATH  Google Scholar 

  7. Postnikov M (1994) Lie groups and Lie algebras. Lectures in geometry, vol V. Nauka, Moscow

    Google Scholar 

  8. van Est WT, Korthagen TJ (1964) Non-enlargeable Lie algebras. Need Akad Wetensch Proc A 26:15–31

    Google Scholar 

  9. Varadarajan VS (1984) Lie groups, Lie algebras and their representations. Springer, New York

    MATH  Google Scholar 

  10. Wald RM (1984) General relativity. The University of Chicago Press, Chicago

    MATH  Google Scholar 

  11. Wilf HS (1986) Algorithms and complexity. Prentice Hall, Upper Saddle River

    MATH  Google Scholar 

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Authors and Affiliations

  1. Dpto. Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, Sevilla, Spain

    Juan Núñez

  2. Dpto. Economía, Métodos Cuantitativos e Historia Económica, Universidad Pablo de Olavide, Sevilla, Spain

    Ángel F. Tenorio

Authors
  1. Juan Núñez
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  2. Ángel F. Tenorio
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Correspondence to Ángel F. Tenorio.

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Núñez, J., Tenorio, Á.F. A computational study of a family of nilpotent Lie algebras. J Supercomput 59, 147–155 (2012). https://doi.org/10.1007/s11227-010-0430-2

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  • DOI: https://doi.org/10.1007/s11227-010-0430-2

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