Vol. 32, No. 1, 1970

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Stability theorems for Lie algebras of derivations

Charles Hallahan

Vol. 32 (1970), No. 1, 105–112

Let A be a finite dimensional algebra over a field F of characteristic zero and let L be a completely reducible Lie algebra of derivations of A. If A is associative, then there exists an L-invariant Wedderburn factor of A. If A is a Lie algebra, there exists an L-invariant Levi factor of A. If A is a solvable Lie algebra, lhere exists an L-invariant Cartan subalgebra of A. This paper deals with the uniqueness of such L-invariant subalgebras. For the associative case the assumption of characteristic zero can be dropped if we assume that the radical of A is L-invariant.

Mathematical Subject Classification
Primary: 17.30
Received: 24 June 1969
Published: 1 January 1970
Charles Hallahan