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Generalized Cayley-Hamilton-Newton identities

A. Isaev·O. Ogievetsky·P. Pyatov
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Abstract

The q-generalizations of the two fundamental statements of matrix algebra -- the Cayley-Hamilton theorem and the Newton relations -- to the cases of quantum matrix algebras of an "RTT-" and of a "Reflection equation" types have been obtained in [2]-[6]. We construct a family of matrix identities which we call Cayley-Hamilton-Newton identities and which underlie the characteristic identity as well as the Newton relations for the RTT- and Reflection equation algebras, in the sence that both the characteristic identity and the Newton relations are direct consequences of the Cayley-Hamilton-Newton identities.

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A. Isaev, O. Ogievetsky, P. Pyatov. 1998-09-09. Generalized Cayley-Hamilton-Newton identities. https://doi.org/10.1023/a:1021649021069

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