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...
Збережено в:
Видавець: | Інститут математики НАН України |
---|---|
Дата: | 2011 |
Автори: | , , |
Формат: | Стаття |
Мова: | English |
Опубліковано: |
Інститут математики НАН України
2011
|
Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147403 |
Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of UkraineРезюме: | 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. |
---|