N-ary Mal'tsev algebras

被引：11
|
作者：
Pozhidaev A.P. [1 ,2 ,3 ]
机构：
[1] National Institute of Occupational Health, N-0033 Oslo
[2] Department of Advanced Materials Science and Engineering, Faculty of Engineering, Yamaguchi University, Ube, 755-8611, Tokiwadai 2557, Yamaguchi
来源：
Algebra and Logic | 2001年 / 40卷 / 3期
关键词：
Mathematical Logic; Cross Product; Basic Result; Natural Generalization; Ground Field;
D O I：
10.1023/A:1010212318874
中图分类号：
学科分类号：
摘要：
By analogy with n-Lie algebras, which are a natural generalization of Lie algebras to the case of n-ary multiplication, we define the concept of an n-ary Mal'tsev algerba. It is shown that exceptional algebras of a vector cross product are ternary central simple Mal'tsev algebras, which are not 3-Lie algebras if the characteristic of a ground field is distinct from 2 and 3. The basic result is that every n-ary algebra of the vector cross product is an n-ary central simple Mal'tsev algebra. © 2001 Plenum Publishing Corporation.
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页码：170 / 182
页数：12
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