scholarly journals Produits de matrices aléatoires et applications aux propriétés géometriques des sous-groupes du groupe linéaire

1990 ◽  
Vol 10 (3) ◽  
pp. 483-512 ◽  
Author(s):  
Yves Guivarc'h
Keyword(s):  
Random Matrices ◽  
Linear Group ◽  
Asymptotic Properties ◽  
Linear Groups ◽  
Products Of Random Matrices ◽  
Free Subgroups

AbstractUsing the asymptotic properties of products of random matrices we study some properties of the subgroups of the linear group. These properties are centered around the theorem of J. Tits giving the existence of free subgroups in linear groups.

scholarly journals Free subgroups in maximal subgroups of skew linear groups

2019 ◽  
Vol 29 (03) ◽  
pp. 603-614 ◽  
Author(s):  
Bui Xuan Hai ◽  
Huynh Viet Khanh
Keyword(s):  
Linear Group ◽  
Division Ring ◽  
General Linear Group ◽  
Subnormal Subgroup ◽  
Free Subgroup ◽  
Maximal Subgroups ◽  
Linear Groups ◽  
Locally Finite ◽  
Starting Point ◽  
Free Subgroups

The study of the existence of free groups in skew linear groups have begun since the last decades of the 20th century. The starting point is the theorem of Tits (1972), now often referred to as Tits’ Alternative, stating that every finitely generated subgroup of the general linear group [Formula: see text] over a field [Formula: see text] either contains a non-cyclic free subgroup or it is solvable-by-finite. In this paper, we study the existence of non-cyclic free subgroups in maximal subgroups of an almost subnormal subgroup of the general skew linear group over a locally finite division ring.

scholarly journals The log-linear group-lasso estimator and its asymptotic properties

Bernoulli ◽  
2012 ◽  
Vol 18 (3) ◽  
pp. 945-974 ◽  
Author(s):  
Yuval Nardi ◽  
Alessandro Rinaldo
Keyword(s):  
Linear Group ◽  
Asymptotic Properties ◽  
Group Lasso ◽  
Log Linear ◽  
Lasso Estimator

scholarly journals Products of random matrices and derivatives on p.c.f. fractals

2008 ◽  
Vol 254 (5) ◽  
pp. 1188-1216 ◽  
Author(s):  
Anders Pelander ◽  
Alexander Teplyaev
Keyword(s):  
Random Matrices ◽  
Products Of Random Matrices

scholarly journals Asymptotic properties of large random matrices with independent entries

1996 ◽  
Vol 37 (10) ◽  
pp. 5033-5060 ◽  
Author(s):  
Alexei M. Khorunzhy ◽  
Boris A. Khoruzhenko ◽  
Leonid A. Pastur
Keyword(s):  
Random Matrices ◽  
Asymptotic Properties

scholarly journals Holomorphic Cohomology of Complex Analytic Linear Groups

1966 ◽  
Vol 27 (2) ◽  
pp. 531-542 ◽  
Author(s):  
G. Hochschild ◽  
G. D. Mostow
Keyword(s):  
Linear Group ◽  
Structure Theory ◽  
Linear Groups ◽  
Dimensional Representation ◽  
Lie Algebra Cohomology ◽  
Analytic Group ◽  
Finite Dimensional Representation ◽  
Semidirect Products ◽  
Finite Dimensional ◽  
Rational Cohomology

Let G be a complex analytic group, and let A be the representation space of a finite-dimensional complex analytic representation of G. We consider the cohomology for G in A, such as would be obtained in the usual way from the complex of holomorphic cochains for G in A. Actually, we shall use a more conceptual categorical definition, which is equivalent to the explicit one by cochains. In the context of finite-dimensional representation theory, nothing substantial is lost by assuming that G is a linear group. Under this assumption, it is the main purpose of this paper to relate the holomorphic cohomology of G to Lie algebra cohomology, and to the rational cohomology, in the sense of [1], of algebraic hulls of G. This is accomplished by using the known structure theory for complex analytic linear groups in combination with certain easily established results concerning the cohomology of semidirect products. The main results are Theorem 4.1 (whose hypothesis is always satisfied by a complex analytic linear group) and Theorems 5.1 and 5.2. These last two theorems show that the usual abundantly used connections between complex analytic representations of complex analytic groups and rational representations of algebraic groups extend fully to the superstructure of cohomology.

Two-Dimensional Linear Groups Over Local Rings

1969 ◽  
Vol 21 ◽  
pp. 106-135 ◽  
Author(s):  
Norbert H. J. Lacroix
Keyword(s):  
Local Ring ◽  
Linear Group ◽  
General Linear Group ◽  
General Linear ◽  
Linear Groups ◽  
Local Rings ◽  
Two Dimensional ◽  
Normal Subgroups ◽  
Field Case

The problem of classifying the normal subgroups of the general linear group over a field was solved in the general case by Dieudonné (see 2 and 3). If we consider the problem over a ring, it is trivial to see that there will be more normal subgroups than in the field case. Klingenberg (4) has investigated the situation over a local ring and has shown that they are classified by certain congruence groups which are determined by the ideals in the ring.Klingenberg's solution roughly goes as follows. To a given ideal , attach certain congruence groups and . Next, assign a certain ideal (called the order) to a given subgroup G. The main result states that if G is normal with order a, then ≧ G ≧ , that is, G satisfies the so-called ladder relation at ; conversely, if G satisfies the ladder relation at , then G is normal and has order .

On the contractibility to a point of the linear groups of reflexive non-commutative Lp-spaces

1996 ◽  
Vol 119 (3) ◽  
pp. 545-560 ◽  
Author(s):  
Sergei V. Ferleger ◽  
Fyodor A. Sukochev
Keyword(s):  
Banach Space ◽  
Linear Group ◽  
Operator Norm ◽  
Linear Groups ◽  
Lp Spaces ◽  
Continuous Map

For every Banach space X, denote by GL(X) the linear group of X, i.e. the group of all linear continuous invertible operators on X with the topology induced by the operator norm. One says that GL(X) is contractible to a point if there exists a continuous map F: GL(X) × [0, 1] → GL(X) such that F(A,0) = A and F(A, 1) = Id, for every A ∈ GL(X).

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