Geodesic
Outer automorphisms of locally simple Lie algebras
Sbornik. Mathematics, Tome 188 (1997) no. 9, pp. 1295-1316

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The automorphism groups of locally simple Lie algebras over $\mathbb C$ are studied. The group of inner automorphisms of such algebras can be defined in a natural way, and it is normal in the automorphisms group. Hence a group of outer automorphisms of a locally simple Lie algebra can be defined. In contact to the finite-dimensional case, it is shown that the group of outer automorphisms is not necessarily finite. It is completely calculated in some special cases. 
@article{SM_1997_188_9_a2,
     author = {D. V. Zhdanovich},
     title = {Outer automorphisms of locally simple {Lie} algebras},
     journal = {Sbornik. Mathematics},
     pages = {1295--1316},
     publisher = {mathdoc},
     volume = {188},
     number = {9},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_9_a2/}
}
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D. V. Zhdanovich. Outer automorphisms of locally simple Lie algebras. Sbornik. Mathematics, Tome 188 (1997) no. 9, pp. 1295-1316. http://geodesic.mathdoc.fr/item/SM_1997_188_9_a2/