Affine Kac-Moody groups and related groups (like loop groups) will be studied from several perspectives. We shall investigate finiteness properties of special linear groups over Laurent polynomials over the ring of integers. We also strive to classify certain maximal Lie orders corresponding to trigonometric solutions of the classical Yang-Baxter equation. In both cases, group actions on affine twin buildings are an essential tool. Such solutions give rise to Lie-Poisson structures on loop groups. The requisite theory of infinite-dimensional Lie-Poisson groups and related Poisson geometry will be developed.
DFG Programme
CRC/Transregios
