Geodesic
Foundations of a theory of dual Lie algebras
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2018), pp. 33-48.

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In this paper we introduce and study dual Lie algebras—Lie algebras over algebra of dual numbers. We prove some fundamental properties of such Lie algebras and track their parallels with properties of usual real and complex Lie algebras. We discuss some results about classification of dual Lie algebra of small dimension and specify connection with the approximate Lie algebras.
Mots-clés : Lie algebra, algebra of dual numbers, dual Lie algebra, approximate Lie algebra. 
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V. V. Gorbatsevich. Foundations of a theory of dual Lie algebras. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2018), pp. 33-48. https://geodesic-test.mathdoc.fr/item/IVM_2018_4_a3/

[1] Ibragimov N. H., CRC handbook of Lie group analysis of differential equations, v. 3, New trends in theoretical development and computational methods, CRC Press, FL, 1996 | MR | Zbl

[2] Gazizov R. K., Lukaschuk V. O., “Klassifikatsii priblizhennykh algebr Li s tremya suschestvennymi vektorami”, Izv. vuzov. Matem., 2010, no. 10, 3–17 | Zbl

[3] Gantmakher F. R., Teoriya matrits, Fizmatlit, M., 2004 | MR

[4] Dixmier J., “Cohomologie des algebres de Lie nilpotentes”, Acta Sci. Math., 16 (1955), 246–250 | MR | Zbl

[5] Gazizov R. K., Lukaschuk V. O., “Klassifikatsiya nepodobnykh priblizhennykh algebr Li s dvumya suschestvennymi simmetriyami na ploskosti”, Tr. pyatoi Vserossiiskoi nauchn. konf. s mezhdunar. uchastiem (29–31 maya 2008 g.), v. 3, Matem. modelirovanie i kraev. zadachi, Differents. uravneniya i kraevye zadachi, SamGTU, Samara, 1–12

[6] Magnin L., “Adjoint and trivial cohomologies of nilpotent complex Lie algebras of dimension $ \le 7$”, Int. J. Math. and Math. Sci., 2008 (1988), 436–450 | MR

[7] Baikov V. A., Gazizov R. K., Ibragimov N. Kh., “Priblizhennye simmetrii”, Matem. sb., 136 (1988), 436–450

[8] Baikov V. A., Gazizov R. K., Ibragimov N. Kh., “Priblizhennye gruppy preobrazovanii”, Differents. uravneniya, 29 (1993), 1712–1732 | Zbl