Geodesic
Real subalgebras in the matrix Lie algebra~$M(2,\mathbf C)$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2010), pp. 30-35

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In this paper we classify all real subalgebras (up to the conjugation) of dimensions 5, 6, and 7 in the Lie algebra of all complex matrices of the second order. In combination with recent results by F. A. Belykh, A. Yu. Borzakov, and A. V. Loboda (Russian Mathematics (Iz. VUZ) 51 (5), 11–23 (2007)) this gives a complete classification of all subalgebras in the specified matrix Lie algebra. The description is presented in two different forms, namely, in the framework of the theory of Lie algebras and their subalgebras, on one hand, and in the matrix form, on the other hand.
Keywords: Lie algebra
Mots-clés : complex matrices, Lie subalgebra, matrix conjugation. 
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     author = {V. V. Gorbatsevich},
     title = {Real subalgebras in the matrix {Lie} algebra~$M(2,\mathbf C)$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {30--35},
     publisher = {mathdoc},
     number = {8},
     year = {2010},
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}
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V. V. Gorbatsevich. Real subalgebras in the matrix Lie algebra~$M(2,\mathbf C)$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2010), pp. 30-35. http://geodesic.mathdoc.fr/item/IVM_2010_8_a2/