Foundations of the Theory of Dual Lie Algebras
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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.
KeywordsLie algebra algebra of dual numbers dual Lie algebra approximate Lie algebra
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- 1.Ibragimov, N. H. CRC Handbook of Lie Group Analysis of Differential Equations. New Trends in Theoretical Development and Computational Methods (CRC Press, FL, 1996), Vol.3.Google Scholar
- 5.Gazizov, R. K. and Lukashchuk, V. O. “Classification of Nonsimilar Approximate Lie Algebras with Two Essential Symmetries on the Plane”, in Proceedings of 5th All-Russia Conference With International Participation (May, 29–31, 2008). Part 3. Differential Equations and Boundary Value Problems,Mathem. modeling and boundary value problems (SamGTU, Samara, 2008), pp. 1–12.Google Scholar
- 8.Baikov, V. A., Gazizov, R. K. and Ibragimov, N. H. “ApproximateGroups of Transformation”, Differ. Equations 29, No. 10, 1487–1504 (1993).Google Scholar