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Can observation offer some hope to Garrett's theory, somehow

  1. Dec 14, 2013 #1


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    The GraviGUT algebra is not a subalgebra of E8, but E8 does contain an Extended GraviGUT algebra

    Andrew Douglas, Joe Repka
    (Submitted on 29 May 2013)
    The GraviGUT algebra is defined as the semidirect sum of spin(11,3) together with its positive chirality 64-dimensional irrep. Recently, Lisi constructed a particular embedding of the GraviGUT algebra into the quaternionic real form of E8. This is not a true Lie algebra embedding since the 64-dimensional irrep of spin(11,3) must be regarded merely as a subset of E8, and not a subalgebra of E8. We prove the stronger statement that the complexified GraviGUT algebra cannot be embedded into the complex algebra E8. We then modify Lisi's construction to create true Lie algebra embeddings of Extended GraviGUT algebras into E8. We classify these embeddings up to inner automorphism. We make no claims on the physical significance of the modified construction.
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