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 G_{A}(R) is the value of the Tits functor G_{A} 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 E_{10}. |