非结合代数是除法的规范。非8维划分线可交换的Jordan代数列的分类
Algebres non associatives normees de division. Classification des algebres reelles de Jordan non commutatives de division lineaire de dimension 8
摘要：
在这项工作中，我们感兴趣的一般问题的确定的赋范划分代数。我们的基本结果是在8维二次柔性实除代数的特定子类中获得的。我们给出了一个新的过程，推广了Cayley-Dickson，并允许获得一个新的家庭的八维二次灵活的实部代数。我们给出的例子8维二次灵活的实部代数不能得到这第一个过程的重复和通过第二个过程，其中包括在作出适当的变形的产品的八元数代数，我们确定这些最后的，我们解决同构问题。在八维二次柔性实除代数中，我们利用广义Cayley-Dickson过程研究了具有非平凡导子的八维二次柔性实除代数。给出了自同构自同构群是平凡的例子，并刻画了自同构自同构群不是平凡的代数。这揭示了这个代数子类的无限性。
英文摘要：
In this work we are interested in the general problem of the determination of the normed division algebras. Our fundamental results are obtained in the particular subclass of those 8-dimensional quadratic flexible real division algebras. We give a new process which generalizes that of Cayley-Dickson and which allows the obtaining of a new family of eight-dimensional quadratic flexible real division algebras. We give examples of 8-dimensional quadratic flexible real division algebras which cannot be obtained by this first process of duplication and by means of a second process, which consists in making an appropriate deformation of the product of the octonion algebra, we determine these last ones and we resolve the isomorphism problem. Among the eight-dimensional quadratic flexible real division algebras, we study those which possess a nontrivial derivation by mean of the generalized Cayley-Dickson process. We also give examples where the group of automorphisms is trivial, and characterize the algebras whose group of automorphisms is not trivial. This brings to light the unlimitedness of this subclass of algebras.
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