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Lie algebras with an algebraic adjoint representation

E. I. Zel'manov


Abstract: 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.

UDC: 519.48

MSC: Primary 17B65; Secondary 17C05

Received: 20.06.1982

 English version: Mathematics of the USSR-Sbornik, 1984, 49:2, 537–552

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