Editing Loop algebra (section)

==Loop group==
Similarly, a set of all smooth maps from {{math|''S''<sup>1</sup>}} to a [[Lie group]] {{math|''G''}} forms an infinite-dimensional Lie group (Lie group in the sense we can define [[functional derivative]]s over it) called the '''[[loop group]]'''. The Lie algebra of a loop group is the corresponding loop algebra.