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Antonov S. Y., Antonova A. V. Quasi-polynomials of Capelli. III. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, vol. 21, iss. 2, pp. 142-150. DOI: 10.18500/1816-9791-2021-21-2-142-150, EDN: HMVRSQ
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. 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 $m\ne k$.
- Antonov S. Yu., Antonova A. V. Quasi-polynomials of Capelli. II. Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics, 2020, vol. 20, iss. 1, pp. 4–16 (in Russian). https://doi.org/10.18500/1816-9791-2020-20-1-4-16
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