The GraviGUT Algebra Is not a Subalgebra of E₈, but E₈ Does Contain an Extended GraviGUT Algebra
The (real) GraviGUT algebra is an extension of the spin(11,3) algebra by a 64-dimensional Lie algebra, but there is some ambiguity in the literature about its definition. Recently, Lisi constructed an embedding of the GraviGUT algebra into the quaternionic real form of E₈. We clarify the definition,...
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| Дата: | 2014 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146626 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The GraviGUT Algebra Is not a Subalgebra of E₈, but E₈ Does Contain an Extended GraviGUT Algebra / A. Douglas, J. Repka // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 13 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146626 |
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dspace |
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irk-123456789-1466262019-02-11T01:24:53Z The GraviGUT Algebra Is not a Subalgebra of E₈, but E₈ Does Contain an Extended GraviGUT Algebra Douglas, A. Repka, J. The (real) GraviGUT algebra is an extension of the spin(11,3) algebra by a 64-dimensional Lie algebra, but there is some ambiguity in the literature about its definition. Recently, Lisi constructed an embedding of the GraviGUT algebra into the quaternionic real form of E₈. We clarify the definition, showing that there is only one possibility, and then prove that the GraviGUT algebra cannot be embedded into any real form of E₈. We then modify Lisi's construction to create true Lie algebra embeddings of the extended GraviGUT algebra into E₈ We classify these embeddings up to inner automorphism. 2014 Article The GraviGUT Algebra Is not a Subalgebra of E₈, but E₈ Does Contain an Extended GraviGUT Algebra / A. Douglas, J. Repka // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 13 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B05; 17B10; 17B20; 17B25; 17B81 DOI:10.3842/SIGMA.2014.072 http://dspace.nbuv.gov.ua/handle/123456789/146626 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The (real) GraviGUT algebra is an extension of the spin(11,3) algebra by a 64-dimensional Lie algebra, but there is some ambiguity in the literature about its definition. Recently, Lisi constructed an embedding of the GraviGUT algebra into the quaternionic real form of E₈. We clarify the definition, showing that there is only one possibility, and then prove that the GraviGUT algebra cannot be embedded into any real form of E₈. We then modify Lisi's construction to create true Lie algebra embeddings of the extended GraviGUT algebra into E₈ We classify these embeddings up to inner automorphism. |
| format |
Article |
| author |
Douglas, A. Repka, J. |
| spellingShingle |
Douglas, A. Repka, J. The GraviGUT Algebra Is not a Subalgebra of E₈, but E₈ Does Contain an Extended GraviGUT Algebra Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Douglas, A. Repka, J. |
| author_sort |
Douglas, A. |
| title |
The GraviGUT Algebra Is not a Subalgebra of E₈, but E₈ Does Contain an Extended GraviGUT Algebra |
| title_short |
The GraviGUT Algebra Is not a Subalgebra of E₈, but E₈ Does Contain an Extended GraviGUT Algebra |
| title_full |
The GraviGUT Algebra Is not a Subalgebra of E₈, but E₈ Does Contain an Extended GraviGUT Algebra |
| title_fullStr |
The GraviGUT Algebra Is not a Subalgebra of E₈, but E₈ Does Contain an Extended GraviGUT Algebra |
| title_full_unstemmed |
The GraviGUT Algebra Is not a Subalgebra of E₈, but E₈ Does Contain an Extended GraviGUT Algebra |
| title_sort |
gravigut algebra is not a subalgebra of e₈, but e₈ does contain an extended gravigut algebra |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146626 |
| citation_txt |
The GraviGUT Algebra Is not a Subalgebra of E₈, but E₈ Does Contain an Extended GraviGUT Algebra / A. Douglas, J. Repka // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 13 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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