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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, Volume 15, Issue 4, Pages 371–382
DOI: https://doi.org/10.18500/1816-9791-2015-15-4-371-382
(Mi isu605)
 

This article is cited in 3 scientific papers (total in 3 papers)

Mathematics

Quasi-polynomials of Capelli

S. Yu. Antonov, A. V. Antonova

Kazan State Power Engineering University, 51, Krasnosel'skaya st., 420066, Kazan, Russia
Full-text PDF (217 kB) Citations (3)
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Abstract: This paper deals with the class of Capelli polynomials in free associative algebra $F\{Z\}$ where $F$ is an arbitrary field and $Z$ is a countable set. The interest to these objects is initiated by assumption that the polynomials (Capelli quasi-polynomials) of some odd degree introduced will be contained in the basis ideal $Z_2$-graded identities of $Z_2$-graded matrix algebra $M^{(m,k)}(F)$ when $\mathrm{char}\,F=0$. In connection with this assumption the fundamental properties of Capelli quasi-polynomials have been given in the paper. In particularly, the decomposition of Capelli type polynomials have been given by the polynomials of the same type and some betweeness of their $T$-ideals have been shown. Besides, taking into account some properties of Capelli quasi-polynomials obtained and also the Chang theorem we show that all Capelli quasi-polynomials of even degree $2n$ $(n>1)$ are consequence of standard polynomial $S_n^-$ in case when the characteristic of field $F$ is not equal to two. At last we find the least $n \in N$ at which any of Capelli quasi-polynomials of even degree $2n$ belongs to ideal of matrix algebra $M_m(F)$ identities.
Key words: $T$-ideal, standard polynomial, Capelli polynomial.
Bibliographic databases:
Document Type: Article
UDC: 512
Language: Russian
Citation: S. Yu. Antonov, A. V. Antonova, “Quasi-polynomials of Capelli”, Izv. Saratov Univ. Math. Mech. Inform., 15:4 (2015), 371–382
Citation in format AMSBIB
\Bibitem{AntAnt15}
\by S.~Yu.~Antonov, A.~V.~Antonova
\paper Quasi-polynomials of Capelli
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2015
\vol 15
\issue 4
\pages 371--382
\mathnet{http://mi.mathnet.ru/isu605}
\crossref{https://doi.org/10.18500/1816-9791-2015-15-4-371-382}
\elib{https://elibrary.ru/item.asp?id=25360653}
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    Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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