Quantized enveloping algebra: Difference between revisions

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In mathematics, a '''quantum''' or '''quantized enveloping algebra''' is a [[Q-analog|''q''-analog]] of a [[universal enveloping algebra]].<ref name="kassel">{{Citation | last1=Kassel | first1=Christian | title=Quantum groups | publisher=[[Springer-Verlag]] | ___location=Berlin, New York | series=[[Graduate Texts in Mathematics]] | isbn=978-0-387-94370-1 | mr=1321145 | year=1995 | volume=155 | url-access=registration | url=https://archive.org/details/quantumgroups0000kass }}</ref> Given a [[Lie algebra]] <math>\mathfrak{g}</math>, the quantum enveloping algebra is typically denoted as <math>U_q(\mathfrak{g})</math>. The notation was introduced by Drinfeld and independently by Jimbo.<ref>{{harvnb|Tjin|1992|loc=§ 5.}}</ref>

Among the applications, studying the <math>q \to 0</math> limit led to the discovery of [[crystal base]]s.

== The case of <math>\mathfrak{sl}_2</math> ==