“Abstract” homomorphisms of split Kac-Moody groups. (English) Zbl 1162.22018
Mem. Am. Math. Soc. 924, 84 p. (2009).
In this paper the author establishes some partial rigidity results for algebraic group actions on twin buildings and applies them to study isomorphisms of Kac-Moody groups over an arbitrary field of cardinality at least four. In particular, the author obtains a detailed description of automorphisms of Kac-Moody groups. He also shows that the Hausdorff topology on a Kac-Moody group is an invariant of the abstract group structure. Finally, the author proves the nonexistence of cocentral homomorphisms of Kac-Moody groups of indefinite type over infinite fields with finite-dimensional target, which provides a partial solution to the linearity problem for Kac-Moody groups.
Reviewer: Volodymyr Mazorchuk (Uppsala)
MSC:
22E65 | Infinite-dimensional Lie groups and their Lie algebras: general properties |
20G15 | Linear algebraic groups over arbitrary fields |
17B40 | Automorphisms, derivations, other operators for Lie algebras and super algebras |
51E24 | Buildings and the geometry of diagrams |