Differential Calculus on h-Deformed Spaces
We construct the rings of generalized differential operators on the h-deformed vector space of gl-type. In contrast to the q-deformed vector space, where the ring of differential operators is unique up to an isomorphism, the general ring of h-deformed differential operators Diffh,σ(n) is labeled by...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2017 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2017
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149274 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Differential Calculus on h-Deformed Spaces / B. Herlemont, O. Ogievetsky // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 22 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862723961160204288 |
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| author | Herlemont, B. Ogievetsky, O. |
| author_facet | Herlemont, B. Ogievetsky, O. |
| citation_txt | Differential Calculus on h-Deformed Spaces / B. Herlemont, O. Ogievetsky // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 22 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We construct the rings of generalized differential operators on the h-deformed vector space of gl-type. In contrast to the q-deformed vector space, where the ring of differential operators is unique up to an isomorphism, the general ring of h-deformed differential operators Diffh,σ(n) is labeled by a rational function σ in n variables, satisfying an over-determined system of finite-difference equations. We obtain the general solution of the system and describe some properties of the rings Diffh,σ(n).
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| first_indexed | 2025-12-07T18:44:59Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149274 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:44:59Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Herlemont, B. Ogievetsky, O. 2019-02-19T19:40:42Z 2019-02-19T19:40:42Z 2017 Differential Calculus on h-Deformed Spaces / B. Herlemont, O. Ogievetsky // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 22 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 16S30; 16S32; 16T25; 13B30; 17B10; 39A14 DOI:10.3842/SIGMA.2017.082 https://nasplib.isofts.kiev.ua/handle/123456789/149274 We construct the rings of generalized differential operators on the h-deformed vector space of gl-type. In contrast to the q-deformed vector space, where the ring of differential operators is unique up to an isomorphism, the general ring of h-deformed differential operators Diffh,σ(n) is labeled by a rational function σ in n variables, satisfying an over-determined system of finite-difference equations. We obtain the general solution of the system and describe some properties of the rings Diffh,σ(n). This paper is a contribution to the Special Issue on Recent Advances in Quantum Integrable Systems. The
 full collection is available at http://www.emis.de/journals/SIGMA/RAQIS2016.html.
 The work of O.O. was supported by the Program of Competitive Growth of Kazan Federal
 University and by the grant RFBR 17-01-00585. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Differential Calculus on h-Deformed Spaces Article published earlier |
| spellingShingle | Differential Calculus on h-Deformed Spaces Herlemont, B. Ogievetsky, O. |
| title | Differential Calculus on h-Deformed Spaces |
| title_full | Differential Calculus on h-Deformed Spaces |
| title_fullStr | Differential Calculus on h-Deformed Spaces |
| title_full_unstemmed | Differential Calculus on h-Deformed Spaces |
| title_short | Differential Calculus on h-Deformed Spaces |
| title_sort | differential calculus on h-deformed spaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149274 |
| work_keys_str_mv | AT herlemontb differentialcalculusonhdeformedspaces AT ogievetskyo differentialcalculusonhdeformedspaces |