Related papers: Property (FA) and lattices in SU(2,1)

We show that cocompact lattices in rank one simple Lie groups of non-compact type distinct from SO(2m,1) (m>0) contain surface subgroups.

Kac-Moody groups over finite fields are finitely generated groups. Most of them can naturally be viewed as irreducible lattices in products of two closed automorphism groups of non-positively curved twinned buildings: those are the most…

An example is given of a compact absolute retract that is not a Hilbert cube manifold but whose second symmetric porduct is the Hilbert cube. A factor theorem is given for nth symmetric product of the cartesian product of any absolute…

Let $G$ be a real centre-free semisimple Lie group without compact factors. I prove that irreducible lattices in $G$ are rigid under two types of sublinear distortions. The first result is that the class of lattices in groups that do not…

A group is LERF (locally extended residually finite) if all its finitely generated subgroups are separable. We prove that the trialitarian arithmetic lattices in $\mathbf{PSO}_{7,1}(\mathbb{R})$ are not LERF. This result, together with…

This paper consists of two parts. In the first part, we prove that when $\mathfrak{g}$ is a simple basic Lie superalgebra with a principal odd nilpotent element $f$, the W-algebra $W^k(\mathfrak{g}, F)$ for $F=-\frac{1}{2}[f,f]$ is…

Given any poset $P$ and chain $\phi$ in $P$, we define the $(P,\phi)$-Tamari lattice. We study in depth these lattices and prove in particular that they are join-semidistributive, join-congruence uniform and left modular. We prove that the…

In a previous work we apply lattice point theorems on hyperbolic spaces obtaining asymptotic formulas for the number of integral representations of negative integers by quadratic and hermitian forms of signature (n,1) lying in Euclidean…

Using a theorem proved by Bekka and Driutti, we show that if $\mathfrak{f}$ is a freely generated nilpotent Lie algebra of step-two, then almost every irreducible representation of the corresponding Lie group restricted to some lattice…

We study profinite actions of residually finite groups in terms of weak containment. We show that two strongly ergodic profinite actions of a group are weakly equivalent if and only if they are isomorphic. This allows us to construct…

We introduce a new iterative amalgamated free product construction of II$_1$ factors, and use it to construct a separable II$_1$ factor which does not have property Gamma and is not elementarily equivalent to the free group factor…

The principle result of this article is the determination of the possible finite subgroups of arithmetic lattices in U(2,1).

We prove the Congruence Subgroup Property for two families of subgroups of Mapping Class Groups of finite-type surfaces. The first one is related to nilpotent quotients of the fundamental group and Johnson filtration, and along the way we…

We provide a complete characterization of pairs of full-rank lattices in $\mathbb{R}^{d}$ which admit common connected fundamental domains of the type $N\left[ 0,1\right) ^{d}$ where $N$ is an invertible matrix of order $d.$ Using our…

The decision problem of membership in the Representation Class of Relation Algebras (RRA) for finite structures is undecidable. However, this does not hold for many Relation Algebra reduct languages. Two well known properties that are…

It was recently proven that the total multiplicity in the decomposition into irreducibles of the tensor product lambda x mu of two irreducible representations of a simple Lie algebra is invariant under conjugation of one of them; at a given…

This is the second in a series of articles surveying the body of work on the model theory of S-acts over a monoid S. The first concentrated on the theory of regular S-acts. Here we review the material on model-theoretic properties of free,…

Relative property (T) has recently been used to construct a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs…

Gr\"atzer and Lakser asked in the 1971 {\sl Transactions of the American Mathematical Society} if the pseudocomplemented distributive lattices in the amalgamation class of the subvariety generated by ${\bf 2}^n\oplus{\bf 1}$ can be…

We introduce and characterize various gluing constructions for residuated lattices that intersect on a common subreduct, and which are subalgebras, or appropriate subreducts, of the resulting structure. Starting from the 1-sum construction…