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Duplication methods for embeddings of real division algebras
Journal of Algebra and Its Applications ( IF 0.5 ) Pub Date : 2020-12-23 , DOI: 10.1142/s0219498822500633 Marina Tvalavadze 1 , Noureddine Motya 2 , Abdellatif Rochdi 2
Journal of Algebra and Its Applications ( IF 0.5 ) Pub Date : 2020-12-23 , DOI: 10.1142/s0219498822500633 Marina Tvalavadze 1 , Noureddine Motya 2 , Abdellatif Rochdi 2
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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 4 D real division algebras. The second process allows us to embed particular classes of 4 D RDAs into 8 D RDAs. Besides, both duplication processes give an infinite family of non-isomorphic 8 D real division algebras whose derivation algebras contain su ( 2 ) .
中文翻译:
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4 D 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8 D RDA。此外,两个复制过程都给出了一个无限的非同构族8 D个实除代数,其导数代数包含苏 ( 2 ) .
更新日期:2020-12-23
中文翻译:
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