Russian Mathematics

, Volume 62, Issue 4, pp 29–41 | Cite as

Foundations of the Theory of Dual Lie Algebras

  • V. V. Gorbatsevich


In this paper we introduce and study dual Lie algebras, i.e., Lie algebras over the algebra of dual numbers. We establish some fundamental properties of such Lie algebras and compare them with the corresponding properties of real and complex Lie algebras. We discuss the question of classification of dual Lie algebras of small dimension and consider the connection of dual Lie algebras with approximate Lie algebras.


Lie algebra algebra of dual numbers dual Lie algebra approximate Lie algebra 


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© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Moscow Aviation Institute (National Research University)MoscowRussia

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