We introduce two groups of duplication processes that extend the well known Cayley–Dickson process. The first one allows to embed every 4-dimensional (4D) real unital algebra 𝒜 into an 8D real unital algebra denoted by FD(𝒜). We also find the conditions on 𝒜 under which FD(𝒜) is a division algebra. This covers the most classes of known 4D real division algebras. The second process allows us to embed particular classes of 4D RDAs into 8D RDAs. Besides, both duplication processes give an infinite family of non-isomorphic 8D real division algebras whose derivation algebras contain su(2).

中文翻译：

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实除法代数嵌入的复制方法

我们介绍了两组复制过程，它们扩展了众所周知的 Cayley-Dickson 过程。第一个允许嵌入每个4维（4D）实单位代数𝒜成一个 8D 实单位代数，表示为FD(𝒜).我们还发现条件𝒜在这之下FD(𝒜)是除法代数。这涵盖了大多数已知类别4D 实除法代数。第二个过程允许我们嵌入特定类别的4将 RDA 纳入8D RDA。此外，两个复制过程都给出了一个无限的非同构族8D个实除代数，其导数代数包含苏(2).