Algebras and Representation Theory

, Volume 14, Issue 1, pp 191-199

First online:

Introduction to Co-split Lie Algebras

  • Limeng XiaAffiliated withFaculty of Science, Jiangsu University
  • , Naihong HuAffiliated withDepartment of Mathematics, East China Normal University Email author 

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In this work, we introduce a new concept which is obtained by defining a new compatibility condition between Lie algebras and Lie coalgebras. With this terminology, we describe the interrelation between the Killing form and the adjoint representation in a new perspective.


Co-split Lie algebra Lie coalgebra Adjoint action

Mathematics Subject Classification (2000)