Embeddings of the Racah Algebra into the Bannai-Ito Algebra
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Embeddings of the Racah Algebra into the Bannai-Ito Algebra
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| Creator |
Genest, V.X.
Vinet, L. Zhedanov, A. |
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| Description |
Embeddings of the Racah algebra into the Bannai-Ito algebra are proposed in two realizations. First, quadratic combinations of the Bannai-Ito algebra generators in their standard realization on the space of polynomials are seen to generate a central extension of the Racah algebra. The result is also seen to hold independently of the realization. Second, the relationship between the realizations of the Bannai-Ito and Racah algebras by the intermediate Casimir operators of the osp(1|2) and su(1,1) Racah problems is established. Equivalently, this gives an embedding of the invariance algebra of the generic superintegrable system on the two-sphere into the invariance algebra of its extension with reflections, which are respectively isomorphic to the Racah and Bannai-Ito algebras.
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| Date |
2019-02-13T16:58:46Z
2019-02-13T16:58:46Z 2015 |
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| Type |
Article
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| Identifier |
Embeddings of the Racah Algebra into the Bannai-Ito Algebra / V.X. Genest, L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 20 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 33C80 DOI:10.3842/SIGMA.2015.050 http://dspace.nbuv.gov.ua/handle/123456789/147119 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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