Vol. 30, No. 1, 1969

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Ideals in admissible algebras

Earl J. Taft

Vol. 30 (1969), No. 1, 259–261

The notion of admissible algebra has been introduced by Koecher. They are commutative algebras whose enveloping Lie algebra (of multiplications) splits into the direct sum of an even and an odd part. It will be shown here that the class of admissible algebras cannot be defined by (nonassociative) polynomial identities. This is done by exhibiting an admissible algebra which possesses a homomorphic image which is not admissible. The main tool is the relationship between the admissibility of a homomorphic image of an admissible algebra A, a symmetry property of a certain ideal of the enveloping Lie algebra of A formed from the kernel of the homomorphism, and the ideal structure of an algebra constructed by Koecher from A.

Mathematical Subject Classification
Primary: 17.60
Received: 23 February 1968
Published: 1 July 1969
Earl J. Taft