The simple non-Lie Malcev algebra as a Lie-Yamaguti algebra

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• 作者：Murray R. Bremner^a ; ^{bremner@math.usask.ca} ; Andrew Douglas^b ; ^{adouglas@citytech.cuny.edu}
• 关键词：Malcev algebras ; Lie&ndash ; Yamaguti algebras ; Nonassociative algebra ; Representation theory ; Polynomial identities ; Computer algebra ; Lattice basis reduction
• 刊名：Journal of Algebra
• 出版年：2012
• 期刊代码：69_00218693
• 类别：mt
• 出版时间：15 May, 2012
• 卷：358
• 期：Complete
• 页码：269-291
• 文件大小：264 K

摘要

The simple 7-dimensional Malcev algebra M is isomorphic to the irreducible -module with binary product defined by the -module morphism . Combining this with the ternary product defined by the -module morphism gives M the structure of a generalized Lie triple system, or Lie-Yamaguti algebra. We use computer algebra to determine the polynomial identities of low degree satisfied by this binary-ternary structure.