Relations Between Combinatorial Structures and Lie Algebras: Centers and Derived Lie Algebras

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• 作者：Manuel Ceballos ; Juan Nú?ez…
• 关键词：Digraph ; Combinatorial structure ; Lie algebra ; Center ; Derived algebra ; 17B60 ; 05C25 ; 05C20 ; 05C90
• 刊名：Bulletin of the Malaysian Mathematical Sciences Society
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：38
• 期：2
• 页码：529-541
• 全文大小：531 KB
• 参考文献：1.Carriazo, A., Fernández, L.M., Nú?ez, J.: Combinatorial structures associated with Lie algebras of finite dimension. Linear Algebra Appl. 389, 43-1 (2004)CrossRef MATH MathSciNet
  2.Ceballos, M., Nú?ez, J., Tenorio, A.F.: Complete triangular structures and Lie algebras. Int. J. Comput. Math. 88, 1839-851 (2011)CrossRef MATH MathSciNet
  3.Ceballos, M., Nú?ez, J., Tenorio, A.F.: Study of Lie algebras by using combinatorial structures. Linear Algebra Appl. 436, 349-63 (2012)CrossRef MATH MathSciNet
  4.Ceballos, M., Nú?ez, J., Tenorio, A.F.: Combinatorial structures and lie algebras of upper-triangular matrices. Appl. Math. Lett. 25, 514-19 (2012)CrossRef MATH MathSciNet
  5.Diestel, R.: Graph Theory, 4th edn. Springer, Heidelberg (2010)CrossRef
  6.Fernández, L.M., Martín-Martínez, L.: Lie algebras associated with triangular configurations. Linear Algebra Appl. 407, 43-3 (2005)CrossRef MATH MathSciNet
  7.Primc, M.: Basic representations for classical affine Lie algebras. J. Algebra 228, 1-0 (2000)CrossRef MATH MathSciNet
  8.Serre, J.P.: Algèbres de Lie Semi-Simples Complexes. Benjamin Inc., New York (1996)
  9.Varadarajan, V.S.: Lie Groups, Lie Algebras and Their Representations. Springer, New York (1984)CrossRef MATH
  
• 作者单位：Manuel Ceballos (1)
  Juan Nú?ez (1)
  ángel F. Tenorio (2)
  
  1. Departamento de Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, Aptdo. 1160, Seville, 41080, Spain
  2. Dpto. de Economía, Métodos Cuantitativos e H.a Económica, Escuela Politécnica Superior, Universidad Pablo de Olavide, Ctra. Utrera km. 1, Seville, 41013, Spain
  
• 刊物类别：Mathematics, general; Applications of Mathematics;
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Singapore
• ISSN：2180-4206

文摘

In this paper, we study how two important ideals of a given Lie algebra \(\mathfrak {g}\) (namely, the center \(Z(\mathfrak {g})\) and the derived Lie algebra \(\mathcal {D}(\mathfrak {g})\)) can be translated into the language of Graph Theory. In this way, we obtain some criteria and characterizations of these ideals using Graph Theory. Keywords Digraph Combinatorial structure Lie algebra Center Derived algebra