Abstract
In this paper the author considers the representation of an algebra L of a certain signature in an algebra A (generally of a different signature) satisfying identity relations of Capelli type. A criterion for the Capelli identities to hold in the pair (A,L) is indicated, and a structural description of such pairs is given. The results are applied for the case where L is a Lie algebra and A is its associative enveloping algebra. In addition, from these results it is deduced that an algebraicity identity over a field of characteristic zero implies nilpotence of the Jacobson radical of a finitely generated associative algebra. Bibliography: 10 titles.
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