Title: General Formulas of the Structure Constants in the $\mathfrak{su}(N)$ Lie Algebra Show Chinese title

Title: 李代数$\mathfrak{su}(N)$的结构常数的一般公式

Abstract: We provide the analytic expressions of the totally symmetric and anti-symmetric structure constants in the $\mathfrak{su}(N)$ Lie algebra. The derivation is based on a relation linking the index of a generator to the indexes of its non-null elements. The closed formulas obtained to compute the values of the structure constants are simple expressions involving those indexes and can be analytically evaluated without any need of the expression of the generators. We hope that these expressions can be widely used for analytical and computational interest in Physics. Show Chinese abstract

Abstract: 我们提供了$\mathfrak{su}(N)$李代数中完全对称和反对称结构常数的解析表达式。 推导基于一个将生成元的指标与其非零元素的指标相联系的关系。 得到的用于计算结构常数值的闭合公式是涉及这些指标的简单表达式，可以无需生成元的表达式进行解析求解。 我们希望这些表达式在物理领域的分析和计算方面得到广泛应用。