From sl_q(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...
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2011-11-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2011.093 |
| _version_ | 1818695571304611840 |
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| author | Satoshi Tsujimoto Luc Vinet Alexei Zhedanov |
| author_facet | Satoshi Tsujimoto Luc Vinet Alexei Zhedanov |
| author_sort | Satoshi Tsujimoto |
| collection | DOAJ |
| 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 sl_q(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. |
| first_indexed | 2024-12-17T13:47:35Z |
| format | Article |
| id | doaj.art-bd06a3ea51204192bce52f02be1c0277 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-17T13:47:35Z |
| publishDate | 2011-11-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-bd06a3ea51204192bce52f02be1c02772022-12-21T21:46:07ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592011-11-017093From sl_q(2) to a Parabosonic Hopf AlgebraSatoshi TsujimotoLuc VinetAlexei ZhedanovA 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 sl_q(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.http://dx.doi.org/10.3842/SIGMA.2011.093parabosonic algebradual Hahn polynomialsClebsch-Gordan coefficients |
| spellingShingle | Satoshi Tsujimoto Luc Vinet Alexei Zhedanov From sl_q(2) to a Parabosonic Hopf Algebra Symmetry, Integrability and Geometry: Methods and Applications parabosonic algebra dual Hahn polynomials Clebsch-Gordan coefficients |
| title | From sl_q(2) to a Parabosonic Hopf Algebra |
| title_full | From sl_q(2) to a Parabosonic Hopf Algebra |
| title_fullStr | From sl_q(2) to a Parabosonic Hopf Algebra |
| title_full_unstemmed | From sl_q(2) to a Parabosonic Hopf Algebra |
| title_short | From sl_q(2) to a Parabosonic Hopf Algebra |
| title_sort | from sl q 2 to a parabosonic hopf algebra |
| topic | parabosonic algebra dual Hahn polynomials Clebsch-Gordan coefficients |
| url | http://dx.doi.org/10.3842/SIGMA.2011.093 |
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