This structure of ℰ8(8) can be understood as follows. The 248-dimensional Lie algebra E8(8) can be represented as 𝔰𝔬(16)⊕ 𝒮16 (direct sum of vector spaces), where 𝒮16 constitutes a 128-dimensional representation space of the group Spin(16), that transforms like Majorana–Weyl spinors. Using Dirac matrices Γ νa μ, the commutation relations read:
[Mab,Mcd ] = δacMbd + δbdMac − adMbc − δbcMad,
1 ν [Mab,Q μ] = 2Γ[ab]μQν,
[Qμ,Q ν] = Γ [ab]Mab. μν
For more information about E8 (8) see [134Jump To The Next Citation Point], and for a general discussion of real forms of Lie algebras see Section 6.