Related papers: Are cluster automorphism groups finitely generated…

It is proved that the generalized cluster complex defined by Fomin and Reading has a dihedral symmetry. Together with diagram symmetries, they generate its automorphism group. A consequence is a simple explicit formula for the order of this…

Given a closed smooth manifold $M$ of even dimension $2n\ge6$ with finite fundamental group, we show that the classifying space ${\rm BDiff}(M)$ of the diffeomorphism group of $M$ is of finite type and has finitely generated homotopy groups…

We present novel constructions concerning the homology of finitely generated groups. Each construction draws on ideas of Gilbert Baumslag. There is a finitely presented acyclic group $U$ such that $U$ has no proper subgroups of finite index…

We completely classify the locally finite, infinite graphs with pure mapping class groups admitting a coarsely bounded generating set. We also study algebraic properties of the pure mapping class group: We establish a semidirect product…

Word metrics on finitely generated groups have canonical quasi-isometry classes, making quasi-isometry invariants genuine group invariants. Rosendal generalized this phenomenon to topological groups through CB-generation, but in the general…

For a subshift over a finite alphabet, a measure of the complexity of the system is obtained by counting the number of nonempty cylinder sets of length $n$. When this complexity grows exponentially, the automorphism group has been shown to…

We show that the conjugacy problem is solvable in [finitely generated free]-by-cyclic groups, by using a result of O. Maslakova that one can algorithmically find generating sets for the fixed subgroups of free group automorphisms, and one…

We will review the main results concerning the automorphism groups of saturated structures which were obtained during the two last decades. The main themes are: the small index property in the countable and uncountable cases; the…

We determine the class group of those generalized cluster algebras that are Krull domains. In particular, this provides a criterion for determining whether or not a generalized cluster algebra is a UFD. In fact, any finitely generated…

We prove that there exist finitely presented, residually finite groups that are profinitely rigid in the class of all finitely presented groups but not in the class of all finitely generated groups. These groups are of the form $\Gamma…

We investigate the general structure of the automorphism group and the Lie algebra of derivations of a finitely generated vertex operator algebra. The automorphism group is isomorphic to an algebraic group. Under natural assumptions, the…

We give a uniform geometric realization for the cluster algebra of an arbitrary finite type with principal coefficients at an arbitrary acyclic seed. This algebra is realized as the coordinate ring of a certain reduced double Bruhat cell in…

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.

In support variety theory, representations of a finite dimensional (Hopf) algebra $A$ can be studied geometrically by associating any representation of $A$ to an algebraic variety using the cohomology ring of $A$. An essential assumption in…

We study adequate subgroups of $GL_n$ over a finite field. This notion is useful in the study of automorphy lifting theorems. In particular, we give a sufficient condition for a subgroup to be adequate.

In this paper we find a necessary and sufficient condition for a finite nilpotent group to have an abelian central automorphism group.

Barbieri recently showed that the finite graphs realising any given finite automorphism group have unbounded genus, answering a question of Cornwell et al. In this note we give a short proof of a stronger result: they have unbounded clique…

We study the automorphisms of graph products of cyclic groups, a class of groups that includes all right-angled Coxeter and right-angled Artin groups. We show that the group of automorphism generated by partial conjugations is itself a…

Cluster algebras are a class of commutative algebras whose generators are defined by a recursive process called mutation. We give a brief introduction to cluster algebras, and explain how discrete integrable systems can appear in the…

We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.