Quantum enveloping algebra
In mathematics, a quantum or quantized enveloping algebra is a q-analog of a universal enveloping algebra. Given a Lie algebra, the quantum enveloping algebra is typically denoted as. Among the applications, studying the limit led to the discovery of crystal bases.The case of
considered the algebras with three generators related by the three commutators
When, these reduce to the commutators that define the special linear Lie algebra. In contrast, for nonzero, 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.
