group theory Classical groups
Cohomology and Extensions
group corresponding to a Kac-Moody algebra is a Kac-Moody group.
This subsumes the case of
affine Lie algebras in which case the corresponding Kac-Moody group is a centrally extended loop group (see there for more) and often the words “Kac-Moody group” are used synonomously with “centrally extended loop group”. Properties
a G G topological group, write for its B G B G delooping, the classifying space for topological - G G principal bundles.
This is due to
Nitu Kitchloo, 1998, see for instance Kitchloo’s survey, p. 9.
Kay moody groups appear as
U-duality groups in 11-dimensional supergravity compactified to low dimensions. References
A standard textbook is
Kac-Moody groups, their flag varieties and representation theory, Progress in Mathematics, 204. Birkhauser Boston, Inc., Boston, MA, (2002)
A survey is
Kac-Moody groups over the last decade ( pdf)
Original articles include
On the Topology of Kac-Moody groups ( arXiv), ( Phd thesis)
Carles Broto, Nitu Kitchloo,
Classifying spaces of Kac-Moody groups, Math. Z. 240,621–649 (2002) ( pdf)
Udo Baumgartner, Jacqueline Ramagge, Bertrand Remy,
Contraction groups in complete Kac-Moody groups (2008) ( pdf)
On the topology and geometry of Kac-Moody groups, PhD thesis (2011) ( web)
Christof Geiss, Bernard Leclerc, Jan Schröer,
Kac-Moody groups and cluster algebras ( arXiv:1001.3545)
Revised on January 19, 2015 15:07:51