Formal Lie groupoids
The notion of Kac-Moody Lie algebra is a generalization of that of semisimple Lie algebra to infinite dimension of the underlying vector space.
The higher Kac-Moody analogs of the exceptional semisimple Lie algebras E7, E7, E8 are
Lecture notes include
The standard textbook is
- Victor Kac, Infinite dimensional Lie algebras, , Cambridge University Press (1990)
Collections of articles include
- N. Sthanumoorty, K. Misra (eds.), Kac-Moody Lie algebras and related topics, Contemporary Mathematics 343 AMS (2002)
The fact that every simply laced hyperbolic Kac-Moody algebra appears as a subalgebra of E10 is in
- Sankaran Viswanath, Embeddings of hyperbolic Kac-Moody algebras into (pdf)
Affine Lie algebras
As far as applications this is the most important class. See Lab entry affine Lie algebra and
- David Hernandez, An introduction to affine Kac-Moody algebras (pdf)
The following references discuss aspects of the Kac-Moody exceptional geometry of supergravity theories.
Revised on June 3, 2012 01:14:05
by Urs Schreiber