Related papers: On flat groups in affine buildings

We use Sigma-invariants to study homotopical and homological finiteness properties of fixed subgroups of automorphisms of a group $G$ in terms of its center $Z(G)$ and the induced automorphisms on its associated quotient $G/Z(G)$.…

We discuss some finite homogeneous structures, addressing the question of universality of their automorphism groups. We also study the existence of so-called Kat\v{e}tov functors in finite categories of embeddings or homomorphisms.

The results of the paper concern the topological structure of complete riemannian manifolds with cyclic holonomy groups and low-dimensional orientable complete flat manifolds. We also discuss related results such as the affine…

Affine Bruhat--Tits buildings are geometric spaces extracting the combinatorics of algebraic groups. The building of $\mathrm{PGL}$ parametrizes flags of subspaces/lattices in or, equivalently, norms on a fixed finite-dimensional vector…

This work introduces author's theory of Bruhat-Tits buildings over higher dimensional local fields. The theory is illustrated with the buildings for PGL(2) and PGL(3) for one- and two-dimensional local fields.

We provide an explicit presentation of the automorphism group of an edge-separated CLTTF Artin group.

In this two-part paper we prove an existence result for affine buildings arising from exceptional algebraic reductive groups. Combined with earlier results on classical groups, this gives a complete and positive answer to the conjecture…

We compute the automorphism group of the affine surfaces with the coordinate ring isomorphic to a cluster algebra of rank 2.

In this paper we introduce, for each closed orientable surface, an analogue of Tits buildings adjusted to investigation of the Torelli group of this surface. It is a simplicial complex with some additional structure. We call this complex…

In this paper we give a self-contained treatment of finite group quotients of admissible (formal) schemes and adic spaces that are locally topologically finite type over a locally strongly noetherian adic space.

We give a classification of maximal elements of the set of finite groups that can be realized as the automorphism groups of polarized abelian threefolds over finite fields.

We find finite presentations for the automorphism group of the Artin pure braid group and the automorphism group of the pure braid group associated to the full monomial group.

We investigate Bruhat-Tits buildings and their compactifications by means of Berkovich analytic geometry over complete non-Archimedean fields. For every reductive group G over a suitable non-Archimedean field k we define a map from the…

We study the problem of classifying local projective structures in dimension two having non trivial Lie symmetries. In particular we obtain a classification of flat projective structures having positive dimensional Lie algebra of projective…

Surface groups are determined among limit groups by their profinite completions. As a corollary, the set of surface words in a free group is closed in the profinite topology.

We introduce a new method to calculate local normal zeta functions of finitely generated, torsion-free nilpotent groups. It is based on an enumeration of vertices in the Bruhat-Tits building for Sl_n(Q_p). It enables us to give explicit…

We prove that for any automorphism $\alpha$ of a free group F of finite rank, one can efficiently compute a basis of the fixed point subgroup Fix(\alpha).

P. Broussous and S. Stevens studied maps between enlarged Bruhat-Tits buildings to construct types for p-adic unitary groups. They needed maps which respect the Moy-Prasad filtrations. That property is called (CLF), i.e. compatibility with…

For bounded pseudoconvex domains with finite type we give a precise description of the automorphism group: if an orbit of the automorphism group accumulates on at least two different points of the boundary, then the automorphism group has…

We study the automorphism groups of finite-dimensional cyclic Leibniz algebras. In this connection, we consider the relationships between groups, modules over associative rings and Leibniz algebras.