Related papers: Dixmier Groups and Borel Subgroups

H\"older's theorem states that any group acting freely by circle homeomorphisms is abelian, this is no longer true for interval exchange transformations: we first give examples of free actions of non abelian groups. Then after noting that…

Let G be a group of automorphisms of a compact K\"ahler manifold X of dimension n and N(G) the subset of null-entropy elements. Suppose G admits no non-abelian free subgroup. Improving the known Tits alternative, we obtain that, up to…

For finitely generated groups $G$ and $H$ equipped with word metrics, a translation-like action of $H$ on $G$ is a free action where each element of $H$ moves elements of $G$ a bounded distance. Translation-like actions provide a geometric…

The symmetric group $\mathsf{S}_n$ and the partition algebra $\mathsf{P}_k(n)$ centralize one another in their actions on the $k$-fold tensor power $\mathsf{M}_n^{\otimes k}$ of the $n$-dimensional permutation module $\mathsf{M}_n$ of…

Let $O_\tau(\Gamma)$ be a family of algebras \textit{quantizing} the coordinate ring of $\mathbb{C}^2 / \Gamma$, where $\Gamma$ is a finite subgroup of $\mathrm{SL}_2(\mathbb{C})$, and let $G_{\Gamma}$ be the automorphism group of $O_\tau$.…

We extend our previous results on generalized Dixmier-Douady theory to graded $C^*$-algebras, as means for explicit computations of the invariants arising for bundles of ungraded $C^*$-algebras. For a strongly self-absorbing $C^*$-algebra…

Let $G$ be a noncompact semisimple algebraic group with trivial center, $S < G$ a maximal split torus, $H < G$ the centralizer of $S$ in $G$ and $\Gamma < G$ an irreducible lattice. Consider the group measure space von Neumann algebra…

We investigate faithful representations of $\operatorname{Alt}(n)$ as automorphisms of a connected group $G$ of finite Morley rank. We target a lower bound of $n$ on the rank of such a nonsolvable $G$, and our main result achieves this in…

All external electromagnetic fields in which the Klein-Gordon-Fock equation admits the first-order symmetry operators are found, provided that in the space-time $V_4$ a group of motion $G_3$ acts simply transitively on a non-null subspace…

We generalize a result of T. Koberda by showing that the natural action of the automorphism group on the space of left-orderings is faithful for all nonabelian bi-orderable groups G, as well as for a certain class of left-orderable groups…

We study the bounded endomorphisms of $\ell_{N}^2(G)=\ell^2(G)\times \dots \times\ell^2(G)$ that commute with translations, where $G$ is a discrete abelian group. It is shown that they form a C*-algebra isomorphic to the C*-algebra of…

It is known that the notion of a transitive subgroup of a permutation group $P$ extends naturally to the subsets of $P$. We study transitive subsets of the wreath product $G \wr S_n$, where $G$ is a finite abelian group. This includes the…

Motivated by work of Poguntke we study the question under what conditions simple subquotients of crossed products $A\rtimes_{\alpha}G$ by (twisted) actions of abelian groups $G$ are isomorphic to simple twisted group algebras of abelian…

We establish an induction isomorphism in the context of measurable bounded cohomology of discrete measured groupoid, which generalizes the Eckmann-Shapiro isomorphism in bounded cohomology of lattices due to Burger and Monod. In our wider…

In this paper we consider non-abelian 1-cohomology for groups with coefficients in other groups. We prove versions of the `five lemma' arising from this situation. We go on to show that a connected unipotent algebraic group Q acted on…

Given a connected reductive algebraic group $G$ with a Borel subgroup $B$ and a quasiaffine spherical $G$-variety $X$, we prove that every $G$-orbit $Y$ contained in the regular locus of $X$ can be connected by a $B$-normalized additive…

Let $G$ be a compact Hausdorff topological group acting on a compact Hausdorff topological space $X$. Within the $C^{*}$-algebra $C(X)$ of all continuous complex-valued functions on $X$, there is the Peter-Weyl algebra $\mathcal{P}_G(X)$…

For a finitely generated group $G$ the Nielsen graph $N_n(G)$, $n\geq \operatorname{rank}(G)$, describes the action of the group $\operatorname{Aut}F_n$ of automorphisms of the free group $F_n$ on generating $n$-tuples of G by elementary…

We treat the problem of finding transitive subgroups G of S_n containing normal subgroups N_1 and N_2, with N_1 transitive and N_2 not transitive, such that G/N_1 is isomorphic G/N_2. We show that such G exist whenever n has a prime factor…

Let $G$ denote a reductive algebraic group over $\mathbb{C}$ and $x$ a nilpotent element of its Lie algebra $\mathfrak{g}$. The Springer variety $\mathcal{B}_x$ is the closed subvariety of the flag variety $\mathcal{B}$ of $G$…