Clifford algebras , with even, are matrix algebras that have a complex representation of dimension . By restricting to the group we get a complex representation of the Pin group of the same dimension, called the spin representation. If we restrict this to the spin group then it splits as the sum of two half spin representations (or Weyl representations) of dimension .
Clifford algebras , with even, are matrix algebras that have a complex representation of dimension . By restricting to the group we get a complex representation of the Pin group of the same dimension, called the spin representation. If we restrict this to the spin group then it splits as the sum of two half spin representations (or Weyl representations) of dimension .