实Clifford代数及其单位群的实矩阵表示

Real Matrix Representations of Real Clifford Algebras and Their Unit Groups

首先,用实Clifford代数的线性变换构造实Clifford代数的单位群Cl^(*)_(0,3),Cl^(*)_(2,1),Cl^(*)_(3,0)的忠实实矩阵表示,发现其为8级实矩阵群的子群;其次,借助实Clifford代数Cl_(p,q)(p+q=3)基元素相互关系及其对应的矩阵关系构建实Clifford代数Cl_(2,1)和Cl_(3,0)的忠实实矩阵表示,发现其为4级实矩阵代数的子代数,并给出其非忠实实矩阵表示.

Firstly,we used the linear transformation of real Clifford algebras to construct the faithful real matrix representations of unit groups of real Clifford algebras Cl^(*)_(0,3),Cl^(*)_(2,1),Cl^(*)_(3,0),and found that they were the subgroups of 8 order real matrix groups.Secondly,we constructed the faithful real matrix representations of real Clifford algebras Cl 2,1 and Cl 3,0 by the relations of basis elements of real Clifford algebras Cl p,q(p+q=3)and their corresponding matrix relations,we found that they were the subalgebras of 4 order real matrix algebras,and gave their unfaithful real matrix representations.