Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

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

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.05.2021
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Russian
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Article
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512
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HMVRSQ

Quasi-polynomials of Capelli. III

Autors: 
Antonova Alina Vladimirovna, Kazan State Power Engineering University, Russia
Abstract: 

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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Received: 
14.02.2020
Accepted: 
01.06.2020
Published: 
31.05.2021