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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2014 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146626 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862545364360364032 |
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| author | Douglas, A. Repka, J. |
| author_facet | Douglas, A. Repka, J. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-25T07:13:08Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146626 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T07:13:08Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Douglas, A. Repka, J. 2019-02-10T10:47:44Z 2019-02-10T10:47:44Z 2014 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 https://nasplib.isofts.kiev.ua/handle/123456789/146626 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. The work of A.D. is partially supported by a research grant from the
 Professional Staf f Congress/ City University of New York (PSC/CUNY). The work of J.R. is
 partially supported by the Natural Sciences and Engineering Research Council (NSERC). The
 authors would also like to thank the anonymous referees for valuable comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The GraviGUT Algebra Is not a Subalgebra of E₈, but E₈ Does Contain an Extended GraviGUT Algebra Article published earlier |
| spellingShingle | The GraviGUT Algebra Is not a Subalgebra of E₈, but E₈ Does Contain an Extended GraviGUT Algebra Douglas, A. Repka, J. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146626 |
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