The structure of : preliminariesIt remains to explain what is .We have to remember the -covariance condition (4) on . It implies that the construction of should be covariant under the local Lorentz transformations . It is convenient to consider complexified symmetry algebras: and . The spinors transform in the fundamental representation of and antifundamental of :

The is characterized as the subalgebra preserving the symplectic forms and , which are both given by the -matrices

This allows to write covariant chains of letters and linked with , for example: