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The GraviGUT Algebra Is not a Subalgebra of E₈, but E₈ Does Contain an Extended GraviGUT Algebra
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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The GraviGUT Algebra Is not a Subalgebra of E₈, but E₈ Does Contain an Extended GraviGUT Algebra
Інший ID:
2010 Mathematics Subject Classification: 17B05; 17B10; 17B20; 17B25; 17B81
DOI:10.3842/SIGMA.2014.072
DOI:10.3842/SIGMA.2014.072
Посилання:
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.
Підтримка:
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.
Дата:
2014
Переглядів:
498
Завантажень:
241
Анотація:
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.
