Quasi-polynomials of Capelli. III
In this paper polynomials of Capelli type (double and quasi-polynomials of Capelli) belonging to a free associative algebra $F\{X\cup Y\}$ considering over an arbitrary field $F$ and generated by two disjoint countable sets $X, Y$ are investigated.&...
Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
Saratov State University
2021-05-01
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Series: | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
Subjects: | |
Online Access: | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2021/05/142-150antonov-antonova.pdf |
Summary: | In this paper polynomials of Capelli type (double and quasi-polynomials of Capelli) belonging to a free associative algebra $F\{X\cup Y\}$ considering over an arbitrary field $F$ and generated by two disjoint countable sets $X, Y$ are investigated. It is shown that double Capelli's polynomials $C_{4k,\{1\}}$, $C_{4k,\{2\}}$ are consequences of the standard polynomial $S^-_{2k}$. Moreover, it is proved that these polynomials equal to zero both for square and for rectangular matrices of corresponding sizes. In this paper it is also shown that all Capelli's quasi-polynomials of the $(4k+1)$ degree are minimal identities of odd component of $Z_2$-graded matrix algebra $M^{(m, k)}(F)$ for any $F$ and $m\ne k$. |
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ISSN: | 1816-9791 2541-9005 |