论文标题
与SO（3）和Quark模型的不可还原张量表示相关的三元代数
Ternary algebras associated with irreducible tensor representations of SO(3) and quark model
论文作者
论文摘要
我们表明，在等级3协变张量的三维空间旋转组的重量2的每个不可还原张量表示会导致与统一性的关联代数。我们发现这些代数的发电机必须满足的代数关系。这些关系的一部分具有二元关系形式，另一部分具有三元关系。三元关系的结构基于循环基团Z_3和Unity Q = \ Exp（2πi/3）的原始立方根。由发电机三重产物跨越的每个代数的子空间是5维，它是旋转组的重量2的不可还原张量表示的空间（3）。我们在这个5维子空间中定义了栖息地标量产品，并为其构建正统基础。然后，我们找到了无穷小旋转的表示矩阵。我们表明，用二进制和三元关系构建代数可以在夸克模型和大统一理论中应用。
We show that each irreducible tensor representation of weight 2 of the rotation group of three-dimensional space in the space of rank 3 covariant tensors gives rise to an associative algebra with unity. We find the algebraic relations that the generators of these algebras must satisfy. Part of these relations has a form of binary relations and another part has a form of ternary relations. The structure of ternary relations is based on the cyclic group Z_3 and the primitive cubic root of unity q=\exp(2πi/3). The subspace of each algebra spanned by the triple products of generators is 5-dimensional and it is the space of an irreducible tensor representation of weight 2 of the rotation group SO(3). We define a Hermitian scalar product in this 5-dimensional subspace and construct an orthonormal basis for it. Then we find the representation matrix of an infinitesimal rotation. We show that constructed algebras with binary and ternary relations can have applications in the quark model and Grand Unification Theories.
