Geodesic
Lie algebras with an algebraic adjoint representation
Sbornik. Mathematics, Tome 49 (1984) no. 2, pp. 537-552

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In this paper it is proved that a Lie algebra over a field of characteristic 0 with an algebraic adjoint representation is locally finite dimensional, provided the algebra satisfies a polynomial identity. In particular, a Lie algebra (over a field of characteristic 0) whose adjoint representation is algebraic of bounded degree is locally finite dimensional. Bibliography: 22 titles. 
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     author = {E. I. Zel'manov},
     title = {Lie algebras with an algebraic adjoint representation},
     journal = {Sbornik. Mathematics},
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     number = {2},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1984_49_2_a16/}
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E. I. Zel'manov. Lie algebras with an algebraic adjoint representation. Sbornik. Mathematics, Tome 49 (1984) no. 2, pp. 537-552. http://geodesic.mathdoc.fr/item/SM_1984_49_2_a16/