In this article we investigate the application of complex split biquaternions and bioctonions to the standard model. We show that the Clifford algebras Cl(3) and Cl(7) can be used for making left-right symmetric fermions. Hence we incorporate right-handed neutrinos in the division algebras-based approach to the standard model. The right-handed neutrinos, or sterile neutrinos, are a potential dark-matter candidate. Using the division algebra approach, we discuss the left-right symmetric fermions and their phenomenology. We describe the gauge groups associated with the left-right symmetric model and prospects for unification through division algebras. We briefly discuss the possibility of obtaining three generations of fermions and charge/mass ratios through the exceptional Jordan algebra \(J_3(O)\) and the exceptional groups \(F_4\) and \(E_6\).

在本文中，我们研究了复杂分裂双四元数和双元数在标准模型中的应用。我们证明 Clifford 代数Cl (3) 和Cl (7) 可用于生成左右对称费米子。因此，我们将右手中微子纳入标准模型的基于除法代数的方法中。右手中微子或惰性中微子是潜在的暗物质候选者。使用除法代数方法，我们讨论左右对称费米子及其现象学。我们描述了与左右对称模型相关的规范组以及通过除代数统一的前景。我们简要讨论通过例外乔丹代数\(J_3(O)\)和例外群\(F_4\)和\(E_6\)获得三代费米子和荷质比的可能性。