# A lightcone construction of the twin building of a hyperbolic Kac-Moody group

*Algebra/Geometry/Topology Seminar*

*by Lisa Carbone*

*Institution:*Rutgers

*Date: Tue 20th December 2011*

*Time: 2:15 PM*

*Location: 213 Richard Berry*

*Abstract*: The Tits building of a group G with a BN-pair is a simplicial complex constructed from group theoretical data. The BN-pair associated to a Kac-Moody group gives rise to a twin building \(B+ \cup B-\) corresponding to the positive and negative roots of the Kac-Moody algebra. We construct an embedding of the twin building associated to a hyperbolic Kac-Moody group over C into the corresponding hyperbolic Kac-Moody algebra. It turns out that the twin building is embedded into the lightcone of the Kac-Moody algebra.