We study the universal enveloping associative conformal algebra for the central extension of a current Lie conformal algebra at the locality level N = 3. A standard basis of defining relations for this algebra is explicitly calculated. As a corollary, we find a linear basis of the free commutative conformal algebra relative to the locality N = 3 on the generators.

中文翻译：

---

Kac-Moody保形代数的通用缔合保形包络的标准基础

我们研究了局部位置N = 3时当前Lie共形代数的中心扩展的通用包络联合共形代数。为该代数定义关系的标准基础已明确计算。作为推论，我们找到了自由可交换保形代数相对于生成器上局部性N = 3的线性基础。