Geodesic
Locally finite-dimensional simple Lie algebras
Sbornik. Mathematics, Tome 81 (1995) no. 1, pp. 137-161

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In this paper the authors introduce a new class of simple infinite-dimensional Lie algebras: locally finite-dimensional Lie algebras. First, general properties of such algebras are studied, and an uncountable family of examples is pointed out. Then the investigation is restricted to simple locally finite-dimensional algebras whose classical finite-dimensional simple factors have totally bounded dimension. The structure of these algebras is determined in the case where the base field is algebraically closed of characteristic $p>7$. 
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     author = {Yu. A. Bahturin and H. Strade},
     title = {Locally finite-dimensional simple {Lie} algebras},
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Yu. A. Bahturin; H. Strade. Locally finite-dimensional simple Lie algebras. Sbornik. Mathematics, Tome 81 (1995) no. 1, pp. 137-161. http://geodesic.mathdoc.fr/item/SM_1995_81_1_a7/