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《Journal of Qinghai Normal University(Natural Science Edition)》 2010-01
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A_4 Algebra and the Triplet Product of Cubic Matrices

YU Rui-yan 1,WANG Tao2(1.School of Information and Mathematics,Yangtzeu University,Jingzhou 434023,China;2.Center for High-Energy Physics,Peking University,Beijing 100871,China)  
Tile Lie-3 algebra is a generalization of ordinary Lie algebra.The most interesting example is A4 algebra,whose mathematical properties deserve further study.In this article,we realize the representation of A4 with cubic matrices.The triplet product for these cubic matrices is defined carefully so that the algebra of cubic matrices coincides with A4 algebra.The matrix representation and its triplet product proposed here are reasonable even if the identity matrix is taken into consideration.
【CateGory Index】: O151.21
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【Co-references】
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