Related papers: Affine buildings for dihedral groups
We construct a finitely generated 2-dimensional group that acts properly on a locally finite CAT(0) cube complex but does not act properly on a finite dimensional CAT(0) cube complex.
We study the singular affine structures of integrable systems with focus-focus singular fibers on the image of momentum maps. The classification of singular affine structures is equivalent to the classification of simple semitoric systems…
We study the possibility of applying a finite-dimensionality argument in order to address parts of the Baum-Connes conjecture for finitely generated linear groups. This gives an alternative approach to the results of Guentner, Higson, and…
We study the pointed or copointed liftings of Nichols algebras associated to affine racks and constant cocycles for any finite group admitting a principal YD-realization of these racks. In the copointed case we complete the classification…
A class of classical affine W-algebras are shown to be isomorphic as differential algebras to the coordinate rings of double coset spaces of certain prounipotent proalgebraic groups. As an application, integrable Hamiltonian hierarchies…
This is a sequel to arXiv:2506.13656, in which an approach to construct a class of generalized Frobenius manifold structures on the orbit spaces of affine Weyl groups is presented. In this paper we apply this construction to the affine Weyl…
In this paper, we describe the structure of finite groups whose element orders or proper (abelian) subgroup orders form an arithmetic progression of ratio $r\geq 2$. This extends the case $r=1$ studied in previous papers \cite{1,8,4}.
We construct 3-manifolds which have at least two inequivalent embeddings such that both complementary regions have abelian fundamental group.
It is shown that a finite group in which more than 3/4 of the elements are involutions must be an elementary abelian 2-group. A group in which exactly 3/4 of the elements are involutions is characterized as the direct product of the…
We classify smooth surfaces whose higher cohomologies of i-forms for all i vanish. We show that if such a surface is not affine, then it has essentially two possibilities.
We classify complex compact parallelizable manifolds which admit flat torsion free holomorphic affine connections. We exhibit complex compact manifolds admitting holomorphic affine connections, but no flat torsion free holomorphic affine…
We provide the first examples of lattices on irreducible buildings that are not residually finite. Assuming that the normal subgroup property holds for them (which is expected) five of the lattices are simple.
We classify surjective self-maps (of degree at least two) of affine surfaces according to the log Kodaira dimension.
Using Singer polygons, we construct locally finite affine buildings of types ~A_2 and ~C_2 which admit uniform lattices acting regularly on panels. This construction produces very explicit descriptions of these buildings as well as very…
For any compact, connected, orientable, finite-type surface with marked points other than the sphere with three marked points, we construct a finite rigid set of its arc complex: a finite simplicial subcomplex of its arc complex such that…
We give a characterization of limits of dihedral groups in the space of finitely generated marked groups. We also describe the topological closure of dihedral groups in the space of marked groups on a fixed number of generators.
We classify the twisted tensor products of a finite set algebra with a two elements set algebra using colored quivers obtained through considerations analogous to Ore extensions. This provides also a classification of entwining structures…
We give very flexible, concrete constructions of discrete and faithful epresentations of right-angled Artin groups into higher-rank Lie groups. Using the geometry of the associated symmetric spaces and the combinatorics of the groups, we…
We prove a prime geodesic theorem for compact quotients of affine buildings and apply it to get class number asymptotics for global fields of positive characteristic.
In this paper, we study wall elements of rank 2 cluster scattering diagrams based on dilogarithm elements. We derive two major results. First, we give a method to calculate wall elements in lower degrees. By this method, we may see the…