THE HURWITZ THEOREM ON SUMS OF SQUARES BY LINEAR
... (More generally, Lj and Lk are anti-commuting for any different j, k > 2.) Viewing L3 and L4 as linear operators not on Cn but on the vector space U 1, their anticommutativity on U forces dim U = n/2 to be even by Lemma 2.1, so n must be a multiple of 4. This eliminates the choice n = 6 and conclude ...
... (More generally, Lj and Lk are anti-commuting for any different j, k > 2.) Viewing L3 and L4 as linear operators not on Cn but on the vector space U 1, their anticommutativity on U forces dim U = n/2 to be even by Lemma 2.1, so n must be a multiple of 4. This eliminates the choice n = 6 and conclude ...
