Geometriae Dedicata

, 136:191 | Cite as

Positive definite Minkowski Lie algebras and bi-invariant Finsler metrics on Lie groups

  • Shaoqiang DengEmail author
  • Zixin Hou
Original Paper


In this paper, we introduce the notion of a Minkowski Lie algebra, which is the natural generalization of the notion of a real quadratic Lie algebra (metric Lie algebra). We then study the positive definite Minkowski Lie algebras and obtain a complete classification of the simple ones. Finally, we present some applications of our results to Finsler geometry and give a classification of bi-invariant Finsler metrics on Lie groups.


Minkowski Lie algebras Quadratic Lie algebras Finsler metrics Compact Lie groups 

Mathematics Subject Classification (2000)

17B20 22E46 53C12 


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.School of Mathematical Sciences and LPMCNankai UniversityTianjinPeople’s Republic of China

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