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.&...
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| Language: | English |
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Saratov State University
2021-05-01
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| Series: | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
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| Online Access: | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2021/05/142-150antonov-antonova.pdf |
| _version_ | 1818730841152421888 |
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| author | Antonov, Stepan Yuryevich Antonova, Alina Vladimirovna |
| author_facet | Antonov, Stepan Yuryevich Antonova, Alina Vladimirovna |
| author_sort | Antonov, Stepan Yuryevich |
| collection | DOAJ |
| description | 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 $m\ne k$. |
| first_indexed | 2024-12-17T23:08:11Z |
| format | Article |
| id | doaj.art-b869787cd4384fbba5eb1a35e2922036 |
| institution | Directory Open Access Journal |
| issn | 1816-9791 2541-9005 |
| language | English |
| last_indexed | 2024-12-17T23:08:11Z |
| publishDate | 2021-05-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
| spelling | doaj.art-b869787cd4384fbba5eb1a35e29220362022-12-21T21:29:11ZengSaratov State UniversityИзвестия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика1816-97912541-90052021-05-0121214215010.18500/1816-9791-2021-21-2-142-150Quasi-polynomials of Capelli. IIIAntonov, Stepan Yuryevich0Antonova, Alina Vladimirovna1Kazan State Power Engineering University, Russia, Russia, 420066, Kazan, Krasnosel'skaya st., 51Kazan State Power Engineering University, Russia, Russia, 420066, Kazan, Krasnosel'skaya st., 51In 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 $m\ne k$.https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2021/05/142-150antonov-antonova.pdft-idealstandard polynomialcapelli polynomial |
| spellingShingle | Antonov, Stepan Yuryevich Antonova, Alina Vladimirovna Quasi-polynomials of Capelli. III Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика t-ideal standard polynomial capelli polynomial |
| title | Quasi-polynomials of Capelli. III |
| title_full | Quasi-polynomials of Capelli. III |
| title_fullStr | Quasi-polynomials of Capelli. III |
| title_full_unstemmed | Quasi-polynomials of Capelli. III |
| title_short | Quasi-polynomials of Capelli. III |
| title_sort | quasi polynomials of capelli iii |
| topic | t-ideal standard polynomial capelli polynomial |
| url | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2021/05/142-150antonov-antonova.pdf |
| work_keys_str_mv | AT antonovstepanyuryevich quasipolynomialsofcapelliiii AT antonovaalinavladimirovna quasipolynomialsofcapelliiii |