Geodesic
Algebras satisfying Capelli identities
Izvestiya. Mathematics , Tome 18 (1982) no. 1, pp. 125-144.

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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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Yu. P. Razmyslov. Algebras satisfying Capelli identities. Izvestiya. Mathematics , Tome 18 (1982) no. 1, pp. 125-144. http://geodesic.mathdoc.fr/item/IM2_1982_18_1_a6/

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