In mathematics, for any Lie algebra L one can construct its universal enveloping algebraU(L). This construction passes from the non-associative structure L to a (more familiar, and possibly easier to handle) unital associative algebra which captures the important properties of L.
![L](/Images/godic/202502/18/d20caec3b48a1eef164cb4ca81ba25875214.png")
的泛包络代数 ![U(L)](/Images/godic/202502/18/0b941f8cf3d583be85bff166b80517715214.png")
。李代数一般并非结合代数，但泛包络代数则是带乘法单比特的结合代数。李代数的表示理论可以理解为其泛包络代数的表示理论。在几何上，泛包络代数可以解释为李群上的左不变微分算子。