用Clifford代数Cl8的子空间表示Spinor空间V8+与V8-,利用这些表示研究Triality变换的性质,并用Triality变换证明Spin7同构于7维Spin群Spin(7),Grassmann流形G(3,7)与G(4,8)的一个子流形CAY同胚.
In this paper,we represent the Spinor space V+8 and V-8 as subspaces of Clifford algebra C8.By these representations we study the Triality transformation.Then we show that the group Spin7 is isomorphic to the Spin group Spin(7),Grassmann manifold G(3,7) is diffeomorphic to CAY which is a submanifold of G(4,8).