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.

引用

页码：170 / 182

页数：12

共 9 条

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[9]

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