# 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.