This structure of
can be understood as follows. The 248-dimensional Lie algebra
can be represented as
(direct sum of vector spaces), where
constitutes a 128-dimensional representation space of the group
, that transforms like Majorana–Weyl spinors. Using Dirac matrices
, the commutation relations
read:
![[Mab,Mcd ] = δacMbd + δbdMac − adMbc − δbcMad,](article2587x.gif)
![1 ν [Mab,Q μ] = 2Γ[ab]μQν,](article2589x.gif)
![[Qμ,Q ν] = Γ [ab]Mab. μν](article2591x.gif)
For more information about
see [134
], and for a general discussion of real forms of Lie algebras see
Section 6.