Algebras and Representation Theory

, Volume 14, Issue 1, pp 191–199

Introduction to Co-split Lie Algebras


  • Limeng Xia
    • Faculty of ScienceJiangsu University
    • Department of MathematicsEast China Normal University

DOI: 10.1007/s10468-009-9183-0

Cite this article as:
Xia, L. & Hu, N. Algebr Represent Theor (2011) 14: 191. doi:10.1007/s10468-009-9183-0


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 algebraLie coalgebraAdjoint action

Mathematics Subject Classification (2000)

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© Springer Science+Business Media B.V. 2009