Abstract
The sequence of cocharacters (c.c.s.) of a P.I. algebra is studied. We prove that an algebra satisfies a Capelli identity if, and only if, all the Young diagrams associated with its cocharacters are of a bounded height. This result is then applied to study the identities of certain P.I. algebras, includingF k .
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S. A. Amitsur,Identities and linear dependence, Israel J. Math.22(1975), 127–137.
Ju. P. Razmyslov,On the Kaplansky problem, Izv. Akad. Nauk SSSR Ser. Mat.37(1973), 483–501 (Russian).
A. Regev,The T-ideal generated by the standard identity s 3 [x 1 , x 2 , x 3 ] Israel J. Math.26(1977), 105–125.
A. Regev,The representations of s n and explicit identities for P.I. algebras, J. Algebra51 (1978), 25–40.
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Regev, A. Algebras satisfying a Capelli identity. Israel J. Math. 33, 149–154 (1979). https://doi.org/10.1007/BF02760555
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DOI: https://doi.org/10.1007/BF02760555