We give an interpretation of the maximal number of linearly independent vector fields on spheres in terms of the Spin(9) representation on R^16 . This casts an insight on the role of Spin(9) as a subgroup of SO(16) on the existence of vector fields on spheres, parallel to the one played by complex, quaternionic and octonionic structures on R^2, R^4 and R^8, respectively.
Spheres with more than 7 vector fields: All the fault of Spin(9)
PARTON, Maurizio
;
2013-01-01
Abstract
We give an interpretation of the maximal number of linearly independent vector fields on spheres in terms of the Spin(9) representation on R^16 . This casts an insight on the role of Spin(9) as a subgroup of SO(16) on the existence of vector fields on spheres, parallel to the one played by complex, quaternionic and octonionic structures on R^2, R^4 and R^8, respectively.File in questo prodotto:
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