For citation:
Antonov S. Y., Antonova A. V. To Chang Theorem. III. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2018, vol. 18, iss. 2, pp. 128-143. DOI: 10.18500/1816-9791-2018-18-2-128-143, EDN: XQFNQD
To Chang Theorem. III
Various multilinear polynomials of Capelli type belonging to a free associative algebra F {X ∪ Y } over an arbitrary field F generated by a countable set X ∪ Y are considered. The formulas expressing coefficients of polynomial Chang R(¯x, ¯y|¯w) are found. It is proved that if the characteristic of field F is not equal two then polynomial R(¯x, ¯y| ¯w) may be represented by different ways in the form of sum of two consequencesof standard polynomial S− (¯x). The decomposition of Chang polynomial H (¯x, ¯y|¯w) different from already known is given. Besides, the connection between polynomials R(¯x, ¯y|¯w) and H (¯x, ¯y|¯w) is found. Some consequences of standard polynomial being of great interest for algebras with polynomial identities are obtained. In particular, a new identity of min imal degree for odd component of Z2 -graded matrix algebra M(m,m) (F) is given.
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