三指标阵空间代数结构.pdf

Classi?ed Index:CODE: 10075U. D. C. :NO.: 20090869A Dissertation for the Degree of Master ScienceAlgebraic Structures of3-IndicesMatrix SpaceCandidate : Zhang MengSupervisor : RuipuAcademic Degree Applied for : Master of ScienceSpeciality : Fundamental MathematicsUniversity : Hebei UniversityDate of Oral Examination : May,20123-3-?15TM(),N-A,3|A|s, s=1, 2, 34<A>t,t= 1,2,3,(),Lrs3-Jrs,F153-3-IAbstractAbstractThe paper mainly concerns multiplicative structures of 3-indices matrix (cubic ma-trix) and algebraic structures of 3-indices matrix space ?. Fifteenkinds of multiplicationsTM() for arbitrary two cubic matrices which satisfying the associative law are pro-vided, and the relationship between di?erent multiplications discussed. For anN-ordercubic matrixA, three kinds of determinant|A|s,s= 1,2,3 and four kinds of ”trace”<A>t,t= 1,2,3,4 are de?nied. According to these multiplicationsTM(), the LiealgebraLrsand 3 - Lie algebraJrsare constructed, respectively, and the structures the paper, the characteristic of a ?eldFis assumed to be zero. anization of the paper is as follows:Section 1 introduces the background and the development of 2 de?nes 15 kinds of multiplications which satisfy the associative 3 de?nes the determinants and traces of the cubic 4 constructs of Lie algebras by cubic 5 constructs of 3-Lie algebras by cubic algebra 3-Lie algebra cubic matrices determinant traceII1.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . 12.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .104.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .-. . . . . . . . .