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[[Michio Jimbo]] considered the algebras with three generators related by the three commutators
:<math>[h,e] = 2e,\ [h,f] = -2f,\ [e,f] = \sinh(\eta h)/\sinh \eta.</math>
When <math>\eta \to 0</math>, these reduce to the commutators that define the [[special linear Lie algebra]] <math>\mathfrak{sl}_2</math>. In contrast, for nonzero <math>\eta</math>, the algebra defined by these relations is not a [[Lie algebra]] but instead an [[associative algebra]] that can be regarded as a deformation of the universal enveloping algebra of <math>\mathfrak{sl}_2</math>.<ref name="jimbo">{{Citation | last=Jimbo |first=Michio |title=A <math>q</math>-difference analogue of <math>U(\mathfrak{g})</math> and the Yang–Baxter equation |journal=[[Letters in Mathematical Physics]] |volume=10 |year=1985 |number=1 |pages=63–69 |doi=10.1007/BF00704588 |authorlink=Michio Jimbo|bibcode=1985LMaPh..10...63J |s2cid=123313856 }}</ref>
== References ==
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