Bekka, M. Bachir
Overview
Works:  17 works in 46 publications in 3 languages and 1,560 library holdings 

Roles:  Author, Opponent, 956 
Classifications:  QA611.5, 515.42 
Publication Timeline
.
Most widely held works by
M. Bachir Bekka
Ergodic theory and topological dynamics of group actions on homogeneous spaces by
M. Bachir Bekka(
Book
)
13 editions published in 2000 in English and held by 297 WorldCat member libraries worldwide
Proof of the Vanishing Theorem for Groups Locally Isomorphic to SL(2, R)Proof of the Vanishing Theorem for General Semisimple Groups; 2 Moore's Ergodicity Theorems; 3 Counting Lattice Points in the Hyperbolic Plane; 4 Mixing of All Orders; Ledrappier's Counterexample; Mixing of All Orders for Actions of Semisimple Groups; Notes; Chapter IV The Horocycle Flow; 1 The Horocycle Flow of a Riemann Surface; Hedlund's Minimality Theorem; 2 Proof of Hedlund's Theorem  Cocompact Case; General Properties of Minimal Invariant Sets; Proof of Hedlund's Theorem  Cocompact Case
13 editions published in 2000 in English and held by 297 WorldCat member libraries worldwide
Proof of the Vanishing Theorem for Groups Locally Isomorphic to SL(2, R)Proof of the Vanishing Theorem for General Semisimple Groups; 2 Moore's Ergodicity Theorems; 3 Counting Lattice Points in the Hyperbolic Plane; 4 Mixing of All Orders; Ledrappier's Counterexample; Mixing of All Orders for Actions of Semisimple Groups; Notes; Chapter IV The Horocycle Flow; 1 The Horocycle Flow of a Riemann Surface; Hedlund's Minimality Theorem; 2 Proof of Hedlund's Theorem  Cocompact Case; General Properties of Minimal Invariant Sets; Proof of Hedlund's Theorem  Cocompact Case
Kazhdan's property (T) by
M. Bachir Bekka(
Book
)
12 editions published in 2008 in English and held by 187 WorldCat member libraries worldwide
A comprehensive introduction to the role of Property (T), with applications to an amazing number of fields within mathematics
12 editions published in 2008 in English and held by 187 WorldCat member libraries worldwide
A comprehensive introduction to the role of Property (T), with applications to an amazing number of fields within mathematics
Ideale mit beschränkten approximativen Einsen in L1Algebren von exponentiellen, auflösbaren LieGruppen by
M. Bachir Bekka(
Book
)
4 editions published in 1983 in German and held by 17 WorldCat member libraries worldwide
4 editions published in 1983 in German and held by 17 WorldCat member libraries worldwide
Phénomènes de rigidité pour un réseau dans un produit de groupes by
Nicolas Louvet(
Book
)
2 editions published between 1998 and 2009 in French and held by 3 WorldCat member libraries worldwide
Une classe remarquable de groupes localement compacts a été découverte par Kazhdan en 1967. Il s'agit des groupes possédant la propriété (t)(appelés aussi groupes de Kazhdan). Ces groupes jouissent d'innombrables propriétés de rigidité et ont des applications en géométrie, théorie des graphes, algèbre d'opérateurs, un groupe g localement compact possède la propriété (t) de Kazhdan si la représentation triviale de dimension un de g est un point isolé dans le dual unitaire de g. De façon équivalente, si le groupe g est dénombrable à l'infini alors g possède la propriété (t) si et seulement si le premier espace de cohomologie de g a coefficients dans une représentation unitaire quelconque est trivial. De plus, un réseau (i.e. un sousgroupe discret de covolume fini) dans un groupe de Kazhdan possède également la propriété (t). Dans ce travail, nous obtenons, pour un réseau irréductible dans le produit direct de deux groupes localement compacts, des résultats du type propriété (t) affaiblie : annulation du premier espace de cohomologie pour une famille de représentations ou isolation de la représentation triviale dans un sous ensemble naturel de représentations, ainsi que des résultats du type superrigidité des représentations : telles représentations du réseau proviennent de restrictions de représentations du groupe ambiant. Nous donnons également quelques conséquences de ces résultats (absence de trace sur la c*algèbre du réseau, rigidité des représentations de dimension finie) ainsi qu'une liste de groupes pour lesquels nos résultats s'appliquent
2 editions published between 1998 and 2009 in French and held by 3 WorldCat member libraries worldwide
Une classe remarquable de groupes localement compacts a été découverte par Kazhdan en 1967. Il s'agit des groupes possédant la propriété (t)(appelés aussi groupes de Kazhdan). Ces groupes jouissent d'innombrables propriétés de rigidité et ont des applications en géométrie, théorie des graphes, algèbre d'opérateurs, un groupe g localement compact possède la propriété (t) de Kazhdan si la représentation triviale de dimension un de g est un point isolé dans le dual unitaire de g. De façon équivalente, si le groupe g est dénombrable à l'infini alors g possède la propriété (t) si et seulement si le premier espace de cohomologie de g a coefficients dans une représentation unitaire quelconque est trivial. De plus, un réseau (i.e. un sousgroupe discret de covolume fini) dans un groupe de Kazhdan possède également la propriété (t). Dans ce travail, nous obtenons, pour un réseau irréductible dans le produit direct de deux groupes localement compacts, des résultats du type propriété (t) affaiblie : annulation du premier espace de cohomologie pour une famille de représentations ou isolation de la représentation triviale dans un sous ensemble naturel de représentations, ainsi que des résultats du type superrigidité des représentations : telles représentations du réseau proviennent de restrictions de représentations du groupe ambiant. Nous donnons également quelques conséquences de ces résultats (absence de trace sur la c*algèbre du réseau, rigidité des représentations de dimension finie) ainsi qu'une liste de groupes pour lesquels nos résultats s'appliquent
Some groups whose reduced C*Algebra is simple by
M. Bachir Bekka(
Book
)
1 edition published in 1993 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 3 WorldCat member libraries worldwide
Représentations unitaires des réseaux dans les groupes de Lie Nilpotents by
Pierre Driutti(
)
2 editions published between 1999 and 2009 in French and held by 2 WorldCat member libraries worldwide
Soit G un groupe de Lie nilpotent, réel, connexe et simplement connexe. Si H est un réseau de G, nous étudions les restrictions à H des représentations unitaires irréductibles de G, ainsi que l'action (par translation à droite) de sousgroupes de G sur la nilvariété H\G
2 editions published between 1999 and 2009 in French and held by 2 WorldCat member libraries worldwide
Soit G un groupe de Lie nilpotent, réel, connexe et simplement connexe. Si H est un réseau de G, nous étudions les restrictions à H des représentations unitaires irréductibles de G, ainsi que l'action (par translation à droite) de sousgroupes de G sur la nilvariété H\G
Conjecture des diviseurs de zéro et propriété (T) by
Christian Masse(
)
2 editions published in 2004 in French and held by 2 WorldCat member libraries worldwide
This work behaves two independent parties : the first chapter draft of the zero divisor conjecture, in the framework of abelian groups, nilpotent groups, semisimple groups and at last discrete groups. In the second chapter, we prove that the group Sp (n,1) has property (T) of Kazhdan of two different manners ; the first proof is based on ideas of M. Cowling and U. Haargerup, the second on ideas of B. Bekka, P. Harpe and A. Valette
2 editions published in 2004 in French and held by 2 WorldCat member libraries worldwide
This work behaves two independent parties : the first chapter draft of the zero divisor conjecture, in the framework of abelian groups, nilpotent groups, semisimple groups and at last discrete groups. In the second chapter, we prove that the group Sp (n,1) has property (T) of Kazhdan of two different manners ; the first proof is based on ideas of M. Cowling and U. Haargerup, the second on ideas of B. Bekka, P. Harpe and A. Valette
Complemented *primitive ideals in L 1 algebras of exponential Lie groups and of motion groups by
Mohammed El Bachir Bekka(
Book
)
1 edition published in 1988 in English and held by 1 WorldCat member library worldwide
1 edition published in 1988 in English and held by 1 WorldCat member library worldwide
Familles de graphes expanseurs et paires de Hecke by
M. Bachir Bekka(
Book
)
1 edition published in 2002 in English and held by 1 WorldCat member library worldwide
1 edition published in 2002 in English and held by 1 WorldCat member library worldwide
Groups with simple reduced C*algebras by
M. Bachir Bekka(
)
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
Dynamique des actions de semigroupes d'endomorphismes sur des nilvariétés by
JeanRomain Heu(
Book
)
1 edition published in 2010 in French and held by 1 WorldCat member library worldwide
The dynamical properties of automorphism groups acting on tori have been widely studied. Nilpotent real Lie groups are a first generalization of abelian real Lie groups. Their quotients by lattices are called nilmanifolds. They generalize the notion of torus. In this thesis, we study the action of groups and semigroups of endomorphisms of some nilmanifolds, such as Heisenberg nilmanifolds. We describe three dynamical aspects of these actions : the density of orbits, the set of invariant measures and the existence of a spectral gap for operators on the Lspaces associated to the nilmanifolds
1 edition published in 2010 in French and held by 1 WorldCat member library worldwide
The dynamical properties of automorphism groups acting on tori have been widely studied. Nilpotent real Lie groups are a first generalization of abelian real Lie groups. Their quotients by lattices are called nilmanifolds. They generalize the notion of torus. In this thesis, we study the action of groups and semigroups of endomorphisms of some nilmanifolds, such as Heisenberg nilmanifolds. We describe three dynamical aspects of these actions : the density of orbits, the set of invariant measures and the existence of a spectral gap for operators on the Lspaces associated to the nilmanifolds
Groups with simple reduced C*algebras by
Pierre de La Harpe(
Book
)
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
Rigidité et nonrigidité d'actions de groupes sur les espaces Lp noncommutatifs by
Baptiste Olivier(
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
We studied rigidity properties and strong nonrigidity properties for group actions on noncommutative Lp spaces. Recently, variants of Kazhdan's property (T) and fixedpoint property (FH) were introduced, respectively called property (TB) and property (FB), and described in terms of orthogonal representations on a Banach space B. We are interested in the case where B is a noncommutative Lp space Lp(M), associated to a von Neumann algebra M. In a first part, we show that if a group has property (T), then it has property (TLp(M)) for any von Neumann algebra M. We deduce that higher rank groups have property (FLp(M)). We show that for some algebras, such as M=B(H), properties (T) and (TLp(M)) are equivalent. By contrast, we characterize groups with property (Tlp), and show that this class of groups is larger than the one with property (T). In a second part, we introduce variants of the Haagerup property (H), namely properties (HLp(M)) and aFLp(M)menability, defined in terms of actions on the space Lp(M). We describe relationships between property (H) and its variant (HLp(M)) for different algebras M. We show that groups with property (H) are aFLp(M)menable for some algebras M, such as the hyperfinite II infinite factor
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
We studied rigidity properties and strong nonrigidity properties for group actions on noncommutative Lp spaces. Recently, variants of Kazhdan's property (T) and fixedpoint property (FH) were introduced, respectively called property (TB) and property (FB), and described in terms of orthogonal representations on a Banach space B. We are interested in the case where B is a noncommutative Lp space Lp(M), associated to a von Neumann algebra M. In a first part, we show that if a group has property (T), then it has property (TLp(M)) for any von Neumann algebra M. We deduce that higher rank groups have property (FLp(M)). We show that for some algebras, such as M=B(H), properties (T) and (TLp(M)) are equivalent. By contrast, we characterize groups with property (Tlp), and show that this class of groups is larger than the one with property (T). In a second part, we introduce variants of the Haagerup property (H), namely properties (HLp(M)) and aFLp(M)menability, defined in terms of actions on the space Lp(M). We describe relationships between property (H) and its variant (HLp(M)) for different algebras M. We show that groups with property (H) are aFLp(M)menable for some algebras M, such as the hyperfinite II infinite factor
Frontières de Poisson d'opération quantiques et trajectoires quantiques by
Bunrith Jacques Lim(
Book
)
1 edition published in 2010 in French and held by 1 WorldCat member library worldwide
Le travail de cette thèse s'inscrit dans l'étude des fondements mathématiques de la théorie quantique de l'information et de la physique quantique, à travers l'étude de l'ensemble des points fixes d'opérateurs quantiques (appelé aussi frontière de Poisson) et l'étude des trajectoires quantiques en dimension infinie. Nous précisons en premier lieu la frontière de Poisson d'un opérateur quantique, puis nous répondons négativement aux conjectures soulevées par Arias et al. [Fixed points of quantum operations, J. Math. Phys. 43, 5872 (2002)] sur la frontière de Poisson d'un opérateur quantique. Dans un second temps, nous identifions la frontière de Poisson noncommutative d'un groupoïde sdiscret mesuré permettant ainsi de retrouver un résultat de moyennabilité de l'extension de Poisson du groupoïde. Enfin nous obtenons des résultats sur la purification asymptotique des trajectoires quantiques à valeurs dans une algèbre fortement compacte
1 edition published in 2010 in French and held by 1 WorldCat member library worldwide
Le travail de cette thèse s'inscrit dans l'étude des fondements mathématiques de la théorie quantique de l'information et de la physique quantique, à travers l'étude de l'ensemble des points fixes d'opérateurs quantiques (appelé aussi frontière de Poisson) et l'étude des trajectoires quantiques en dimension infinie. Nous précisons en premier lieu la frontière de Poisson d'un opérateur quantique, puis nous répondons négativement aux conjectures soulevées par Arias et al. [Fixed points of quantum operations, J. Math. Phys. 43, 5872 (2002)] sur la frontière de Poisson d'un opérateur quantique. Dans un second temps, nous identifions la frontière de Poisson noncommutative d'un groupoïde sdiscret mesuré permettant ainsi de retrouver un résultat de moyennabilité de l'extension de Poisson du groupoïde. Enfin nous obtenons des résultats sur la purification asymptotique des trajectoires quantiques à valeurs dans une algèbre fortement compacte
Irreducibility of unitary group representations and reproducing kernels Hilbert spaces by
M. Bachir Bekka(
Book
)
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
On Mackey's irreducibility criterion for induced representations by
M. Bachir Bekka(
)
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
Théorie ergodique des actions de groupes et algèbres de von Neumann by
Alessandro Carderi(
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
This dissertation is about measured group theory, sofic entropy and operator algebras. More precisely, we will study actions of groups on probability spaces, some fundamental properties of their sofic entropy (for countable groups), their full groups (for Polish groups) and the amenable subalgebras of von Neumann algebras associated with hyperbolic groups and lattices of Lie groups. This dissertation is composed of three parts.The first part is devoted to the study of sofic entropy of profinite actions. Sofic entropy is an invariant for actions of sofic groups defined by L. Bowen that generalize Kolmogorov's entropy. The definition of sofic entropy makes use of a fixed sofic approximation of the group. We will show that the sofic entropy of profinite actions does depend on the chosen sofic approximation for free groups and some lattices of Lie groups. The second part is based on a joint work with François Le Maître. The content of this part is based on a prepublication in which we generalize the notion of full group to probability measure preserving actions of Polish groups, and in particular, of locally compact groups. We define a Polish topology on these full groups and we study their basic topological properties, such as the topological rank and the density of aperiodic elements. The third part is based on a joint work with Rémi Boutonnet. The content of this part is based on two prepublications in which we try to understand when the von Neumann algebra of a maximal amenable subgroup of a countable group is itself maximal amenable. We solve the question for hyperbolic and relatively hyperbolic groups using techniques due to Popa. With different techniques, we will then present a dynamical criterion which allow us to answer the question for some amenable subgroups of lattices of Lie groups of higher rank
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
This dissertation is about measured group theory, sofic entropy and operator algebras. More precisely, we will study actions of groups on probability spaces, some fundamental properties of their sofic entropy (for countable groups), their full groups (for Polish groups) and the amenable subalgebras of von Neumann algebras associated with hyperbolic groups and lattices of Lie groups. This dissertation is composed of three parts.The first part is devoted to the study of sofic entropy of profinite actions. Sofic entropy is an invariant for actions of sofic groups defined by L. Bowen that generalize Kolmogorov's entropy. The definition of sofic entropy makes use of a fixed sofic approximation of the group. We will show that the sofic entropy of profinite actions does depend on the chosen sofic approximation for free groups and some lattices of Lie groups. The second part is based on a joint work with François Le Maître. The content of this part is based on a prepublication in which we generalize the notion of full group to probability measure preserving actions of Polish groups, and in particular, of locally compact groups. We define a Polish topology on these full groups and we study their basic topological properties, such as the topological rank and the density of aperiodic elements. The third part is based on a joint work with Rémi Boutonnet. The content of this part is based on two prepublications in which we try to understand when the von Neumann algebra of a maximal amenable subgroup of a countable group is itself maximal amenable. We solve the question for hyperbolic and relatively hyperbolic groups using techniques due to Popa. With different techniques, we will then present a dynamical criterion which allow us to answer the question for some amenable subgroups of lattices of Lie groups of higher rank
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Related Identities
 Mayer, Matthias (Mathematician)
 La Harpe, Pierre de Author
 Valette, Alain
 Kazhdan, D.
 Université de Metz
 University of New South Wales School of Mathematics
 Université européenne de Bretagne
 École doctorale Mathématiques, informatique, signal, électronique et télécommunications (Rennes)
 Louvet, Nicolas (1972....). Author
 Cowling, M. (Michael) 1949