Title: Finite presentation of hyperbolic Kac-Moody groups over rings
Speaker: Lisa Carbone (Rutgers University)
Abstract: Kac-Moody groups are `infinite dimensional' analogs of Lie groups associated to Kac-Moody algebras. When R is a commutative ring, for any symmetrizable generalized Cartan matrix A, the Kac-Moody group GA(R) is the value of the Tits functor GA over R. This abstract definition of Tits is axiomatic in nature and not amenable to computation or to applications. We construct Kac-Moody groups over arbitrary commutative rings using an analog of Chevalley's constructions in finite dimensions and Garland's constructions in the affine case. We give a finite presentation for an important class of Kac-Moody groups including E10.