On algebras satisfying x2x2=N(x)x

被引：14
|
作者：
Elduque, A [1 ]
Okubo, S
机构：
[1] Univ Zaragoza, Fac Ciencias, Dept Matemat, E-50009 Zaragoza, Spain
[2] Univ Rochester, Dept Phys & Astron, Rochester, NY 14627 USA
来源：
MATHEMATISCHE ZEITSCHRIFT | 2000年 / 235卷 / 02期
关键词：
D O I：
10.1007/s002090000151
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The commutative algebras satisfying the "adjoint identity": x(2)x(2) = N(x)x, where N is a cubic form, are shown to be related to a class of generically algebraic Jordan algebras of degree at most 4 and to the pseudo-composition algebras. They are classified under a nondegeneracy condition. As byproducts, the associativity of the norm of any pseudo-composition algebra is proven and the unital commutative and power-associative algebras of degree less than or equal to 3 are shown to be Jordan algebras. Mathematics Subject Classification (1991):17C50, 17A30.
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页码：275 / 314
页数：40
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