Related papers: Elementary groups in $\PSL(3,\C)$

In this article we provide an algebraic characterization of those groups of $PSL(3,\Bbb{C})$ whose limit set in the Kulkarni sense has, exactly, four lines in general position. Also we show that, for this class of groups, the equicontinuity…

In this article we present an example of a discrete group $\Sigma_\C\subset PSL(3,\Bbb{R})$ whose action on $\P^2$ does no have invariant projective subspaces, is not conjugated to complex hyperbolic group and its limit set in the sense of…

Given a discret subgroup $\Gamma\subset PSL(3,\C)$, we determine the number of complex lines and complex lines in general position lying in the complement of: maximal regions on which $\Gamma$ acts properly discontinuously, the Kularni's…

We consider the natural action of the quaternionic projective linear group $\mathrm{PSL}(n+1,\mathbb{H})$ on the quaternionic projective space $\mathbb{P}^n_{\mathbb{H}}$. We compute the Kulkarni limit sets for the cyclic subgroups of…

In this work we study and provide a full description, up to a finite index subgroup, of the dynamics of solvable complex Kleinian subgroups of PSL(3,C). These groups havesimpledynamics, contrary to strongly irre-ducible groups. Because of…

We study three problems related to the limit sets of discrete subgroups of PSL(n+1,C). In Chapter 2, we study the dynamics of solvable discrete subgroups of PSL(n+1,C). We prove that solvable groups are virtually triangularizable and we…

In this paper, we consider the natural action of $\mathrm{SL}(3, \mathbb{H})$ on the quaternionic projective space $ \mathbb{P}_{\mathbb{H}}^2$. Under this action, we investigate limit sets for cyclic subgroups of $\mathrm{SL}(3,…

We compare different notions of limit sets for the action of Kleinian groups on the $n-$dimensional projective space via the irreducible representation $\varrho:PSL(2,\mathbb{C})\to PSL(n+1,\mathbb{C}).$ In particular, we prove that if the…

If $\Gamma$ is a discrete subgroup of $PSL(3,\Bbb{C})$, it is determined the equicontinuity region $Eq(\Gamma)$ of the natural action of $\Gamma$ on $\Bbb{P}^2_\Bbb{C}$. It is also proved that the action restricted to $Eq(\Gamma)$ is…

We study and classify the purely parabolic discrete subgroups of $PSL(3,\Bbb{C})$. This includes all discrete subgroups of the Heisenberg group ${\rm Heis}(3,\Bbb{C})$. While for $PSL(2,\Bbb{C})$ every purely parabolic subgroup is Abelian…

We present a partial classification of those finite linear spaces $\mathcal{S}$ on which an almost simple group $G$ with socle $PSL(3,q)$ acts line-transitively.

We identify the class of elementary groups: the smallest class of totally disconnected locally compact second countable (t.d.l.c.s.c.) groups that contains the profinite groups and the discrete groups, is closed under group extensions of…

We give a topological description of the quotient space $\Omega(G)/G$ in the case $G \subset PSL(3, \mathbb{C})$ is a discrete subgroup acting on $\mathbb{P}^2_\mathbb{C}$ and the maximum number of complex projective lines in general…

We complete the classification of the finite special linear groups $\SL_n(q)$ which are $(2,3)$-generated, i.e., which are generated by an involution and an element of order $3$. This also gives the classification of the finite simple…

We study finite groups arising from configurations of pairwise skew lines in $\mathbb{P}^3_K$. To such a configuration ${L}$ one associates a group $G_{L}\subset \mathrm{PGL}_2(K)$ acting on each line, and we investigate which finite…

Classical Kleinian groups are discrete subgroups of $PSL(2,\C)$ acting on the complex projective line $\P^1$, which actually coincides with the Riemann sphere, with non-empty region of discontinuity. These can also be regarded as the…

In this paper we give a description of the possible limit sets of finitely generated subgroups of irreducible lattices in $PSL(2,R)^r$.

We classify elementary abelian 2 subgroups of compact simple Lie groups of adjoint type. This finishes the classification of elementary abelian $p$ subgroups of compact (or linear algebraic) simple groups of adjoint type.

We consider three families of groups: the Bianchi groups SL(2,O) where O is the ring of integers of an imaginary, quadratic field; the groups SL*(2,O) where O is a *-order of a definite, rational quaternion algebra with an orthogonal…

While lattices in semi-simple Lie groups are studied very well, only little is known about discrete subgroups of infinite covolume. The main class of examples are Schottky groups. Here we investigate some new examples. We consider subgroups…