Quantized enveloping algebra

In mathematics, a quantum or quantized enveloping algebra is a q-analog of a universal enveloping algebra.^[1] Given a Lie algebra ${\displaystyle {\mathfrak {g}}}$, the quantum enveloping algebra is typically denoted as ${\displaystyle U_{q}({\mathfrak {g}})}$. The notation was introduced by Drinfeld and independently by Jimbo.^[2]

Among the applications, studying the ${\displaystyle q\to 0}$ limit led to the discovery of crystal bases.