31 citations · 61 across the 12 of their papers we have counts for
13 papers
Combinatorial Characterizations of Virtually Torsion-Free and Virtually Free Groups
R. Köhl, M. Reza Salarian
We establish combinatorial characterizations of virtually torsion-free and virtually free groups using the canonical graph decomposition theory in \cite{DJKK22}. Our main results s…
On convexity and the Iwasawa decomposition of split real and complex Kac-Moody groups
Paul Zellhofer, Ralf Köhl
We prove an analogue of Kostant's convexity theorem for split real and complex Kac-Moody groups associated to free and cofree root data. The result can be seen as a first step towa…
Representations of involutory subalgebras of affine Kac-Moody algebras
Axel Kleinschmidt, Ralf Köhl, Robin Lautenbacher +1
We consider the subalgebras of split real, non-twisted affine Kac-Moody Lie algebras that are fixed by the Chevalley involution. These infinite-dimensional Lie algebras are not of…
Fundamental groups of split real Kac-Moody groups and generalized real flag manifolds. With appendices by Tobias Hartnick and Ralf Köhl and by Julius Grüning and Ralf Köhl
Paula Harring, Ralf Köhl
We determine the fundamental groups of symmetrizable algebraically simply connected split real Kac-Moody groups endowed with the Kac-Peterson topology. In analogy to the finite-dim…
Extending generalized spin representations
Robin Lautenbacher, Ralf Köhl
We revisit the construction of higher spin representations by Kleinschmidt and Nicolai for E10, generalize it to arbitrary simply laced types, and provide a coordinate-free approac…
Spin covers of maximal compact subgroups of Kac-Moody groups and spin-extended Weyl groups
David Ghatei, Max Horn, Ralf Köhl +1
Let G be a split real Kac-Moody group of arbitrary type and let K be its maximal compact subgroup, i.e. the subgroup of elements fixed by a Cartan-Chevalley involution of G. We con…
Classifying spaces with virtually cyclic stabilizers for linear groups
Dieter Degrijse, Ralf Köhl, Nansen Petrosyan
We show that every discrete subgroup of admits a finite dimensional classifying space with virtually cyclic stabilizers. Applying our methods to $\mathr…
Quotients of trees for arithmetic subgroups of PGL2 over a rational function field
Ralf Köhl, Bernhard Mühlherr, Koen Struyve
In this note we compute the fundamental domain of the action on the corresponding Bruhat-Tits tree of the arithmetic subgroup of PGL2 with respect to an arbitrary place of the rati…
On topological twin buildings and topological split Kac-Moody groups
Tobias Hartnick, Ralf Köhl, Andreas Mars
We prove that a two-spherical split Kac-Moody group over a local field naturally provides a topological twin building in the sense of Kramer. This existence result and the local-to…
Higher finiteness properties of reductive arithmetic groups in positive characteristic: the rank theorem
Kai-Uwe Bux, Ralf Köhl, Stefan Witzel
We show that the finiteness length of an -arithmetic subgroup in a noncommutative isotropic absolutely almost simple group over a global function field is one less than…
The sphericity of the Phan geometries of type Bn and Cn and the Phan-type theorem of type F4
Ralf Köhl, Stefan Witzel
We adapt and refine methods developed by Abramenko and Devillers--Köhl--Mühlherr in order to establish the sphericity of the Phan geometries of type B_n and C_n, and their generali…
The real quadrangle of type E6
Torsten Kurth, Ralf Köhl, Linus Kramer
We give a geometric interpretation of the building associated to the real Lie group E_6(-14) in terms of its 54-dimensional module.
Defining amalgams of compact Lie groups
Ralf Köhl
For let be a Dynkin diagram of rank and let be the set of labels of . A group admits a weak Phan system of type over i…