Related papers: Aut(F2) puzzles
We investigate the combinatorial and geometric properties of automorphism groups of universal right-angled Coxeter groups, which are the automorphism groups of free products of copies of Z_2. It is currently an open question as to whether…
We show that the following problems are decidable in a rank 2 free group F_2: does a given finitely generated subgroup H contain primitive elements? and does H meet the orbit of a given word u under the action of G, the group of…
We compute the automorphism group of the affine surfaces with the coordinate ring isomorphic to a cluster algebra of rank 2.
For a representative class of subgroups of F_r, the image of their stabilizer subgroup under the action of Aut(F_r) in GL_r(Z) is calculated.
In [HJLLZ24], we proposed a new conjecture on the structure of the unitary dual of connected reductive groups over non-Archimedean local fields of characteristic zero based on their Arthur representations and verified it for all the known…
In this paper, for a Lie 2-algebra $\g$, we construct the automorphism 2-group $\Aut(\g)$, which turns out to be an integration of the derivation Lie 2-algebra $\Der(\g)$.
This paper gives a quick overview of the author's recent result that all finitely presented groups are QSF.
We discuss several arithmetic aspects of Bianchi groups, especially from a computational point of view. In particular, we consider computing the homology of Bianchi groups together with the Hecke action, connections with automorphic forms,…
In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.
In this paper we describe all group gradings by a finite abelian group $\Gamma$ of a simple Lie algebra of type $G_2$ over an algebraically closed field $F$ of characteristic 0.
The holomorph of a free group $F_n$ is the semidirect product $F_n \rtimes Aut(F_n)$. Using the methods of Hatcher and Vogtmann, we derive stability results and calculate the mod-$p$ homology of these holomorphs for odd primes $p$ in…
In this paper we give the characterization of Fuchsian groups acting on quaternionic hyperbolic 2-space.
We give a description of the automorphism group of a Rauzy diagram as a subgroup of the symmetric group. This is based on an example that appear in some personnal notes of Yoccoz that are to be published in the project ''Yoccoz archives''.
We study commensurating actions of groups and the associated properties FW and PW, in connection with wallings, median graphs, CAT(0) cubings and multi-ended Schreier graphs.
Interval type-2 fuzzy logic systems (IT2 FLSs) have a wide range of applications due to their abilities to handle uncertainties compared to their type-1 counterparts. This paper discusses the representation of IT2 FLSs in closed…
We compute the $K$-theory groups of the groupoid C$^\ast$-algebra of the chair tiling, using a new method. We use exact sequences of Putnam to compute these groups from the $K$-theory groups of the $AF$-algebras of the substitution and the…
We define Euclidean scissor congruence groups for an arbitrary algebraically closed field F and propose their conjectural description. We suggest how they should be related to mixed Tate motives over dual numbers for F.
Motivated by topological quantum field theory, we investigate the geometric aspects of unitary 2-representations of finite groups on 2-Hilbert spaces, and their 2-characters. We show how the basic ideas of geometric quantization are…
This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…
We construct extensions of the field of rational numbers with the Galois group G_2(F_p) by reducing p-adic representations attached to automorphic representations.