Vol. 32, No. 2, 1970

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Composition series in Chevalley algebras

James Frederick Hurley

Vol. 32 (1970), No. 2, 429–434

This paper continues the study of how the ideal structure of a Chevalley algebra (a Lie algebra obtained by transferring the scalars of a finite dimensional simple Lie algebra over C to a commutative ring R with identity in which 2 and 3 are not zero divisors) depends on the ideal structure of R. Specifically, we find that composition series of ideals for the Chevalley algebras exist only in case R has composition series of ideals, and in the latter case give explicit descriptions of the composition series in the Chevalley algebras. We also give a necessary and sufficient condition for the composition series in the algebra to exactly parallel those in the ring.

Mathematical Subject Classification
Primary: 17.30
Received: 16 May 1969
Published: 1 February 1970
James Frederick Hurley