Editing Universal enveloping algebra (section)

===Formalities===
The formal construction of the universal enveloping algebra takes the above ideas, and wraps them in notation and terminology that makes it more convenient to work with. The most important difference is that the free associative algebra used in the above is narrowed to the [[tensor algebra]], so that the product of symbols is understood to be the [[tensor product]]. The commutation relations are imposed by constructing a [[Quotient space (linear algebra)|quotient space]] of the tensor algebra quotiented by the ''smallest'' [[two-sided ideal]] containing elements of the form <math>x_i x_j -x_j x_i-\Sigma c_{ijk}x_k</math>. The universal enveloping algebra is the "largest" [[unital associative algebra]] generated by elements of <math>\mathfrak g</math> with a [[Lie bracket]] compatible with the original Lie algebra.