论文标题
约旦代数的分解问题。申请
The factorization problem for Jordan algebras. Applications
论文作者
论文摘要
我们研究了约旦代数设置的分类问题以及分类的补充问题。介绍了匹配的约旦代数和相应的两种产品。结果表明，通过两个给定的约旦代数分解的任何约旦代数对与相同两个约旦代数之间的一对匹配对相关的两种匹配的产物都是同构的。此外，提出了一种新型的约旦代数变形，作为解决分类补充问题的主要步骤。
We investigate the factorization problem as well as the classifying complements problem in the setting of Jordan algebras. Matched pairs of Jordan algebras and the corresponding bicrossed products are introduced. It is shown that any Jordan algebra which factorizes through two given Jordan algebras is isomorphic to a bicrossed product associated to a certain matched pair between the same two Jordan algebras. Furthermore, a new type of deformation of a Jordan algebra is proposed as the main step towards solving the classifying complements problem.
