From slq(2) to a Parabosonic Hopf Algebra
A Hopf algebra with four generators among which an involution (reflection) operator, is introduced. The defining relations involve commutators and anticommutators. The discrete series representations are developed. Designated by sl₋₁(2), this algebra encompasses the Lie superalgebra osp(1|2). It is...
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| Дата: | 2011 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147403 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | From slq(2) to a Parabosonic Hopf Algebra / S. Tsujimoto, L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 24 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147403 |
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dspace |
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irk-123456789-1474032019-02-15T01:24:11Z From slq(2) to a Parabosonic Hopf Algebra Tsujimoto, S. Vinet, L. Zhedanov, A. A Hopf algebra with four generators among which an involution (reflection) operator, is introduced. The defining relations involve commutators and anticommutators. The discrete series representations are developed. Designated by sl₋₁(2), this algebra encompasses the Lie superalgebra osp(1|2). It is obtained as a q=−1 limit of the slq(2) algebra and seen to be equivalent to the parabosonic oscillator algebra in irreducible representations. It possesses a noncocommutative coproduct. The Clebsch-Gordan coefficients (CGC) of sl₋₁(2) are obtained and expressed in terms of the dual −1 Hahn polynomials. A generating function for the CGC is derived using a Bargmann realization. 2011 Article From slq(2) to a Parabosonic Hopf Algebra / S. Tsujimoto, L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 24 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B37; 17B80; 33C45 http://dspace.nbuv.gov.ua/handle/123456789/147403 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
A Hopf algebra with four generators among which an involution (reflection) operator, is introduced. The defining relations involve commutators and anticommutators. The discrete series representations are developed. Designated by sl₋₁(2), this algebra encompasses the Lie superalgebra osp(1|2). It is obtained as a q=−1 limit of the slq(2) algebra and seen to be equivalent to the parabosonic oscillator algebra in irreducible representations. It possesses a noncocommutative coproduct. The Clebsch-Gordan coefficients (CGC) of sl₋₁(2) are obtained and expressed in terms of the dual −1 Hahn polynomials. A generating function for the CGC is derived using a Bargmann realization. |
| format |
Article |
| author |
Tsujimoto, S. Vinet, L. Zhedanov, A. |
| spellingShingle |
Tsujimoto, S. Vinet, L. Zhedanov, A. From slq(2) to a Parabosonic Hopf Algebra Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Tsujimoto, S. Vinet, L. Zhedanov, A. |
| author_sort |
Tsujimoto, S. |
| title |
From slq(2) to a Parabosonic Hopf Algebra |
| title_short |
From slq(2) to a Parabosonic Hopf Algebra |
| title_full |
From slq(2) to a Parabosonic Hopf Algebra |
| title_fullStr |
From slq(2) to a Parabosonic Hopf Algebra |
| title_full_unstemmed |
From slq(2) to a Parabosonic Hopf Algebra |
| title_sort |
from slq(2) to a parabosonic hopf algebra |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147403 |
| citation_txt |
From slq(2) to a Parabosonic Hopf Algebra / S. Tsujimoto, L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 24 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
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2025-07-11T02:01:27Z |
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2025-07-11T02:01:27Z |
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