Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Quantized enveloping algebra
open-in-new
<p>In mathematics, a quantum or quantized enveloping algebra is a <a href="/facts/Q-analog/7jXz12AP"><i>q</i>-analog</a> of a <a href="/facts/Universal_enveloping_algebra/VJ3Syz4W">universal enveloping algebra</a>. Given a <a href="/facts/Lie_algebra/n2gAUkNq">Lie algebra</a> g {\displaystyle {\mathfrak {g}}} , the quantum enveloping algebra is typically denoted as U q ( g ) {\displaystyle U_{q}({\mathfrak {g}})} . The notation was introduced by Drinfeld and independently by Jimbo. </p><p>Among the applications, studying the q → 0 {\displaystyle q\to 0} limit led to the discovery of <a href="/facts/Crystal_base/sb1qXgwa">crystal bases</a>. </p>