Finite-Dimensional Irreducible Modules of the Racah Algebra at Characteristic Zero
Assume that is an algebraically closed field with characteristic zero. The Racah algebra ℜ is the unital associative -algebra defined by generators and relations in the following way. The generators are A, B, C, D, and the relations assert that [A, B]=[B, C]=[C, A]=2D and that each of [A, D]+AC−B...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210592 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Finite-Dimensional Irreducible Modules of the Racah Algebra at Characteristic Zero. Hau-Wen Huang and Sarah Bockting-Conrad. SIGMA 16 (2020), 018, 17 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | Assume that is an algebraically closed field with characteristic zero. The Racah algebra ℜ is the unital associative -algebra defined by generators and relations in the following way. The generators are A, B, C, D, and the relations assert that [A, B]=[B, C]=[C, A]=2D and that each of [A, D]+AC−BA, [B, D]+BA−CB, [C, D]+CB−AC is central in ℜ. In this paper, we discuss the finite-dimensional irreducible ℜ-modules in detail and classify them up to isomorphism. To do this, we apply an infinite-dimensional ℜ-module and its universal property. We additionally give the necessary and sufficient conditions for A, B, C to be diagonalizable on finite-dimensional irreducible ℜ-modules.
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| ISSN: | 1815-0659 |