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Antonov S. Y., Antonova A. V. To Chang Theorem. II. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2017, vol. 17, iss. 2, pp. 127-137. DOI: 10.18500/1816-9791-2017-17-2-127-137, EDN: ZEVWYX
To Chang Theorem. II
Multilinear polynomials H +(¯x, ¯y| ¯ w), H −(¯x, ¯y| ¯ w) ∈ F{X ∪ Y }, the sum of which is a polynomial H (¯x, ¯y| ¯ w) Chang (where F{X∪Y } is a free associative algebra over an arbitrary field F of characteristic not equal two, generated by a countable set X ∪ Y ) have been introduced in this paper. It has been proved that each of them is a consequence of the standard polynomial S−(¯x). In particular it has been shown that the Capelli quasi-polynomials b2m−1(¯xm, ¯y) and h2m−1(¯xm, ¯y) are also consequences of the polynomial S−m (¯x). The minimal degree of the polynomials b2m−1(¯xm, ¯y), h2m−1(¯xm, ¯y) in which they are a polynomial identity of matrix algebra Mn(F) has been also found in the paper. The obtained results are the translation of Chang results to some Capelli quasi polynomials of odd degree.
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