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.
Keywords: Lie algebra, algebra of dual numbers, dual Lie algebra, approximate Lie algebra. 
@article{IVM_2018_4_a3,
     author = {V. V. Gorbatsevich},
     title = {Foundations of a theory of dual {Lie} algebras},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {33--48},
     publisher = {mathdoc},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_4_a3/}
}
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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. http://geodesic.mathdoc.fr/item/IVM_2018_4_a3/