1016/S0096-3003(99)00140-X Raoul E. Cawagas, et al. (2009)., "THE BASIC SUBALGEBRA STRUCTURE OF THE CAYLEY-DICKSON ALGEBRA OF DIMENSION 32 (TRIGINTADUONIONS)"
^{[0]}(V,Q)} 為 C l ( V , Q ) {\displaystyle \mathrm {Cl} (V,Q)} 的子代數(英语:subalgebra),稱為偶子代數。而子空間 C l [ 1 ] ( V , Q ) {\displaystyle \mathrm {Cl} ^{[1]}(V