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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2011 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2011
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147403 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-147403 |
|---|---|
| record_format |
dspace |
| spelling |
Tsujimoto, S. Vinet, L. Zhedanov, A. 2019-02-14T17:43:42Z 2019-02-14T17:43:42Z 2011 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 https://nasplib.isofts.kiev.ua/handle/123456789/147403 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. The authors are grateful to M.S. Plyushchay for drawing their attention to [5] and [14]. The authors would like to gratefully acknowledge the hospitality extended to LV and AZ by Kyoto University and to ST and LV by the Donetsk Institute for Physics and Technology in the course of this investigation. The research of ST is supported in part through funds provided by KAKENHI (22540224), JSPS. The research of LV is supported in part by a research grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications From slq(2) to a Parabosonic Hopf Algebra Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
From slq(2) to a Parabosonic Hopf Algebra |
| spellingShingle |
From slq(2) to a Parabosonic Hopf Algebra Tsujimoto, S. Vinet, L. Zhedanov, A. |
| 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 |
| author |
Tsujimoto, S. Vinet, L. Zhedanov, A. |
| author_facet |
Tsujimoto, S. Vinet, L. Zhedanov, A. |
| publishDate |
2011 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.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. |
| work_keys_str_mv |
AT tsujimotos fromslq2toaparabosonichopfalgebra AT vinetl fromslq2toaparabosonichopfalgebra AT zhedanova fromslq2toaparabosonichopfalgebra |
| first_indexed |
2025-12-07T20:48:18Z |
| last_indexed |
2025-12-07T20:48:18Z |
| _version_ |
1850883962976600064 |