On Multiple Polynomials of Capelli Type
This paper deals with the class of Capelli polynomials in free associative algebra F{Z} (where F is an arbitrary field, Z is a countable set) generalizing the construction of multiple Capelli polynomials. The fundamental properties of the introduced Capelli polynomials are provided. In particular, d...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2016-03-01
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| Series: | Учёные записки Казанского университета. Серия Физико-математические науки |
| Subjects: | |
| Online Access: | http://kpfu.ru/portal/docs/F1262480853/158_1_phys_mat_1.pdf |
| _version_ | 1797964973258833920 |
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| author | S.Y. Antonov A.V. Antonova |
| author_facet | S.Y. Antonov A.V. Antonova |
| author_sort | S.Y. Antonov |
| collection | DOAJ |
| description | This paper deals with the class of Capelli polynomials in free associative algebra F{Z} (where F is an arbitrary field, Z is a countable set) generalizing the construction of multiple Capelli polynomials. The fundamental properties of the introduced Capelli polynomials are provided. In particular, decomposition of the Capelli polynomials by means of the same type of polynomials is shown. Furthermore, some relations between their T -ideals are revealed. A connection between double Capelli polynomials and Capelli quasi-polynomials is established. |
| first_indexed | 2024-04-11T01:52:56Z |
| format | Article |
| id | doaj.art-4ca5f48cc51b49c6a9883ca94406e9b4 |
| institution | Directory Open Access Journal |
| issn | 2541-7746 2500-2198 |
| language | English |
| last_indexed | 2024-04-11T01:52:56Z |
| publishDate | 2016-03-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета. Серия Физико-математические науки |
| spelling | doaj.art-4ca5f48cc51b49c6a9883ca94406e9b42023-01-03T05:53:57ZengKazan Federal UniversityУчёные записки Казанского университета. Серия Физико-математические науки2541-77462500-21982016-03-011581525On Multiple Polynomials of Capelli TypeS.Y. Antonov0A.V. Antonova1Kazan State Power Engineering University, Kazan, 420066 RussiaKazan State Power Engineering University, Kazan, 420066 RussiaThis paper deals with the class of Capelli polynomials in free associative algebra F{Z} (where F is an arbitrary field, Z is a countable set) generalizing the construction of multiple Capelli polynomials. The fundamental properties of the introduced Capelli polynomials are provided. In particular, decomposition of the Capelli polynomials by means of the same type of polynomials is shown. Furthermore, some relations between their T -ideals are revealed. A connection between double Capelli polynomials and Capelli quasi-polynomials is established.http://kpfu.ru/portal/docs/F1262480853/158_1_phys_mat_1.pdfmatrix algebraCapelli polynomialpolynomial identityfree associative algebrasymmetric groupstandard polynomialT -idea |
| spellingShingle | S.Y. Antonov A.V. Antonova On Multiple Polynomials of Capelli Type Учёные записки Казанского университета. Серия Физико-математические науки matrix algebra Capelli polynomial polynomial identity free associative algebra symmetric group standard polynomial T -idea |
| title | On Multiple Polynomials of Capelli Type |
| title_full | On Multiple Polynomials of Capelli Type |
| title_fullStr | On Multiple Polynomials of Capelli Type |
| title_full_unstemmed | On Multiple Polynomials of Capelli Type |
| title_short | On Multiple Polynomials of Capelli Type |
| title_sort | on multiple polynomials of capelli type |
| topic | matrix algebra Capelli polynomial polynomial identity free associative algebra symmetric group standard polynomial T -idea |
| url | http://kpfu.ru/portal/docs/F1262480853/158_1_phys_mat_1.pdf |
| work_keys_str_mv | AT syantonov onmultiplepolynomialsofcapellitype AT avantonova onmultiplepolynomialsofcapellitype |