Affine Lie-Algebra

An affine Lie algebra in mathematics is an infinite-dimensional Lie algebra, which is constructed in a canonical way from a finite-dimensional simple Lie algebra.

Definition

Let be a finite-dimensional finite Lie algebra. Then the associated affine Lie algebra is defined as the vector space

With the commutator relation

For. Here, the Lie bracket in and the Killing form of.

• Lie algebra