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In mathematics, a quantum or quantized enveloping algebra is a q-analog of a universal enveloping algebra. Given a Lie algebra g {\displaystyle {\mathfrak {g}}} , the quantum enveloping algebra is typically denoted as U q {\displaystyle U_{q}}. Among the applications, studying the q → 0 {\displaystyle q\to 0} limit led to the discovery of crystal bases.
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