In mathematics, an affine Lie algebra is a Kac-Moody algebra whose generalized Cartan matrix is of rank 1.

The representation theory of affine Lie algebras is much better understood than that of general Kac-Moody algebras. Also, they appear naturally in theoretical physics (for example, conformal field theory), geometry, and elsewhere in mathematics.

References

• Jurgen Fuchs, Affine Lie Algebras and Quantum Groups, (1992) Cambridge University Press. ISBN 0-521-48412-X