The Racah Algebra as a Subalgebra of the Bannai-Ito Algebra
Assume that is a field with char ≠ 2. The Racah algebra ℜ is a unital associative -algebra defined by generators and relations. The generators are A, B, C, D, and the relations assert that [A, B]=[B, C]=[C, A]=2D, and each of [A, D]+AC−BA, [B, D]+BA−CB, [C, D]+CB−AC is central in ℜ. The Bannai-Ito...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210773 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The Racah Algebra as a Subalgebra of the Bannai-Ito Algebra. Hau-Wen Huang. SIGMA 16 (2020), 075, 15 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862715010595160064 |
|---|---|
| author | Huang, Hau-Wen |
| author_facet | Huang, Hau-Wen |
| citation_txt | The Racah Algebra as a Subalgebra of the Bannai-Ito Algebra. Hau-Wen Huang. SIGMA 16 (2020), 075, 15 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Assume that is a field with char ≠ 2. The Racah algebra ℜ is a unital associative -algebra defined by generators and relations. The generators are A, B, C, D, and the relations assert that [A, B]=[B, C]=[C, A]=2D, and each of [A, D]+AC−BA, [B, D]+BA−CB, [C, D]+CB−AC is central in ℜ. The Bannai-Ito algebra is a unital associative -algebra generated by X, Y, Z, and the relations assert that each of {X, Y}−Z, {Y, Z}−X, {Z, X}−Y is central in I. It was discovered that there exists an -algebra homomorphism ζ: ℜ → that sends A↦(2X−3)(2X+1)/16, B↦(2Y−3)(2Y+1)16, C↦(2Z−3)(2Z+1)/16. We show that ζ is injective and therefore ℜ can be considered as an -subalgebra of . Moreover, we show that any Casimir element of ℜ can be uniquely expressed as a polynomial in {X, Y} − Z, {Y, Z} − X, {Z, X} − Y, and X + Y + Z with coefficients in .
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| first_indexed | 2026-03-20T06:42:49Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210773 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-20T06:42:49Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Huang, Hau-Wen 2025-12-17T14:35:43Z 2020 The Racah Algebra as a Subalgebra of the Bannai-Ito Algebra. Hau-Wen Huang. SIGMA 16 (2020), 075, 15 pages 1815-0659 2020 Mathematics Subject Classification: 81R10; 81R12 arXiv:1906.11745 https://nasplib.isofts.kiev.ua/handle/123456789/210773 https://doi.org/10.3842/SIGMA.2020.075 Assume that is a field with char ≠ 2. The Racah algebra ℜ is a unital associative -algebra defined by generators and relations. The generators are A, B, C, D, and the relations assert that [A, B]=[B, C]=[C, A]=2D, and each of [A, D]+AC−BA, [B, D]+BA−CB, [C, D]+CB−AC is central in ℜ. The Bannai-Ito algebra is a unital associative -algebra generated by X, Y, Z, and the relations assert that each of {X, Y}−Z, {Y, Z}−X, {Z, X}−Y is central in I. It was discovered that there exists an -algebra homomorphism ζ: ℜ → that sends A↦(2X−3)(2X+1)/16, B↦(2Y−3)(2Y+1)16, C↦(2Z−3)(2Z+1)/16. We show that ζ is injective and therefore ℜ can be considered as an -subalgebra of . Moreover, we show that any Casimir element of ℜ can be uniquely expressed as a polynomial in {X, Y} − Z, {Y, Z} − X, {Z, X} − Y, and X + Y + Z with coefficients in . The research is supported by the Ministry of Science and Technology of Taiwan under the project MOST 106-2628-M-008-001-MY4. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Racah Algebra as a Subalgebra of the Bannai-Ito Algebra Article published earlier |
| spellingShingle | The Racah Algebra as a Subalgebra of the Bannai-Ito Algebra Huang, Hau-Wen |
| title | The Racah Algebra as a Subalgebra of the Bannai-Ito Algebra |
| title_full | The Racah Algebra as a Subalgebra of the Bannai-Ito Algebra |
| title_fullStr | The Racah Algebra as a Subalgebra of the Bannai-Ito Algebra |
| title_full_unstemmed | The Racah Algebra as a Subalgebra of the Bannai-Ito Algebra |
| title_short | The Racah Algebra as a Subalgebra of the Bannai-Ito Algebra |
| title_sort | racah algebra as a subalgebra of the bannai-ito algebra |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210773 |
| work_keys_str_mv | AT huanghauwen theracahalgebraasasubalgebraofthebannaiitoalgebra AT huanghauwen racahalgebraasasubalgebraofthebannaiitoalgebra |