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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMar 31st 2019
• (edited Mar 31st 2019)
• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeMay 17th 2019

• Maurizio Parton, Paolo Piccinni, The Role of Spin(9) in Octonionic Geometry, (arXiv:1810.06288)
• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeDec 26th 2019

and this text:

The exact gauge group of the standard model of particle physics (see there) is isomorphic to the subgroup of the Jordan algebra automorphism group of the octonionic Albert algebra that “stabilizes a 4d sub-Minkowski spacetime” (see there for details).

More concretely, it is identified with the subgroup of Spin(9) which respects a splitting $\mathbb{H} \oplus \mathbb{H} \simeq_{\mathbb{R}} \mathbb{C} \oplus \mathbb{C}^3$ (Krasnov 19)

• CommentRowNumber4.
• CommentAuthorDavid_Corfield
• CommentTimeFeb 26th 2020

A couple more references

• Thomas Friedrich, Weak Spin(9)-Structures on 16-dimensional Riemannian Manifolds, (arXiv:math/9912112)

• Maurizio Parton, Paolo Piccinni, Spin(9) and almost complex structures on 16-dimensional manifolds, (arXiv:1105.5318)