弦和膜连接的超矩阵因子
Hypermatrix factors for string and membrane junctions
摘要：
经典群SU（n）、SO（n）和Sp（n）的李代数的伴随表示分别是两个向量空间的张量、反对称和对称积，因此是矩阵表示。我们考虑了三个向量空间的类积，并研究了它们在李代数分解中何时作为和项出现。例外李代数的Z3-分次提供了这样的和项，并提供了超矩阵上的经典群的表示。主要的自然应用是正式研究弦和膜的三结。还考虑了一般化。
英文摘要：
The adjoint representations of the Lie algebras of the classical groups SU(n), SO(n), and Sp(n) are, respectively, tensor, antisymmetric, and symmetric products of two vector spaces, and hence are matrix representations. We consider the analogous products of three vector spaces and study when they appear as summands in Lie algebra decompositions. The Z3-grading of the exceptional Lie algebras provide such summands and provides representations of classical groups on hypermatrices. The main natural application is a formal study of three-junctions of strings and membranes. Generalizations are also considered.
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