Algebras and Representation Theory

, Volume 14, Issue 1, pp 191–199

Introduction to Co-split Lie Algebras

Article

Abstract

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.

Keywords

Co-split Lie algebra Lie coalgebra Adjoint action 

Mathematics Subject Classification (2000)

17B62 

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References

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    Etingof, P., Kazhdan, D.: Quantization of Lie bialgebras, I. Sel. Math. (N.S.) 2(1), 1–41 (1996)MATHCrossRefMathSciNetGoogle Scholar
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    Etingof, P., Kazhdan, D.: Quantization of Lie bialgebras, II. Sel. Math. (N.S.) 4(2), 213–231 (1998)MATHCrossRefMathSciNetGoogle Scholar
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    Etingof, P., Schiffmann, O.: Lectures on Quantum Groups. Internat. Press, Boston (1998)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Faculty of ScienceJiangsu UniversityZhenjiangPeople’s Republic of China
  2. 2.Department of MathematicsEast China Normal UniversityShanghaiPeople’s Republic of China

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