The GraviGUT Algebra Is not a Subalgebra of E8, but E8 Does Contain an Extended GraviGUT Algebra
نویسنده
چکیده
The (real) GraviGUT algebra is an extension of the spin(11, 3) algebra by a 64dimensional 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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