Outer automorphisms of locally simple Lie algebras

D. V. Zhdanovich

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 512.554

MSC: Primary 17B40; Secondary 17B65, 17B20, 22E60, 18B99

Received: 29.11.1996

DOI: 10.4213/sm256

 English version: Sbornik: Mathematics, 1997, 188:9, 1295–1316

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