∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Related topics
Examples
-Lie groupoids
-Lie groups
-Lie algebroids
-Lie algebras
The notion of Kac-Moody Lie algebra is a generalization of that of semisimple Lie algebra to infinite dimension of the underlying vector space.
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The sequence of exceptional semisimple Lie algebras E7, E7, E8 may be continued to the Kac-Moody algebras:
On the Wess-Zumino-Witten model 2d CFT via Kac-Moody algebra and Virasoro algebra:
See also:
Lecture notes include
Antony Wassermann, Kac-Moody and Virasoro algebras, course notes (2011) (pdf)
Hermann Nicolai, Infinite dimensional symmetries (2009) (pdf)
The standard textbook is
Collections of articles include
Surveys include
The fact that every simply laced hyperbolic Kac-Moody algebra appears as a subalgebra of E10 is in
As far as applications this is the most important class. See Lab entry affine Lie algebra and
The following references discuss aspects of the Kac-Moody exceptional geometry of supergravity theories.
Hermann Nicolai, Infinite dimensional symmetries (2009) (pdf)
Paul Cook, Connections between Kac-Moody algebras and M-theory PhD thesis (arXiv:0711.3498)
Daniel Persson, Nassiba Tabti, Lectures on Kac-Moody Algebras with Applications in (Super-)Gravity (pdf)
Last revised on January 20, 2023 at 11:16:27. See the history of this page for a list of all contributions to it.