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. (C) 2012 Elsevier Inc. All rights reserved.
Spheres with more than 7 vector fields: All the fault of Spin(9) / Maurizio, Parton; Piccinni, Paolo. - In: LINEAR ALGEBRA AND ITS APPLICATIONS. - ISSN 0024-3795. - STAMPA. - 438:3(2013), pp. 1113-1131. [10.1016/j.laa.2012.06.046]
Spheres with more than 7 vector fields: All the fault of Spin(9)
PICCINNI, Paolo
2013
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. (C) 2012 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
