Lubotzky, Alexander 1956
Overview
Works:  8 works in 80 publications in 4 languages and 1,673 library holdings 

Roles:  Author, Editor 
Classifications:  QA178, 512.2 
Publication Timeline
.
Most widely held works by
Alexander Lubotzky
Discrete groups, expanding graphs, and invariant measures by
Alexander Lubotzky(
Book
)
32 editions published between 1989 and 2010 in 3 languages and held by 400 WorldCat member libraries worldwide
Presents the solutions to two problems: the first is the construction of expanding graphs  graphs which are of fundamental importance for communication networks and computer science, and the second is the Ruziewicz problem concerning the finitely additive invariant measures on spheres
32 editions published between 1989 and 2010 in 3 languages and held by 400 WorldCat member libraries worldwide
Presents the solutions to two problems: the first is the construction of expanding graphs  graphs which are of fundamental importance for communication networks and computer science, and the second is the Ruziewicz problem concerning the finitely additive invariant measures on spheres
Tree lattices by
Hyman Bass(
Book
)
14 editions published between 2000 and 2001 in English and held by 307 WorldCat member libraries worldwide
Group actions on trees furnish a unified geometric way of recasting the chapter of combinatorial group theory dealing with free groups, amalgams, and HNN extensions. Some of the principal examples arise from rank one simple Lie groups over a nonarchimedean local field acting on their BruhatTits trees. In particular this leads to a powerful method for studying lattices in such Lie groups. This monograph extends this approach to the more general investigation of Xlattices G, where Xis a locally finite tree and G is a discrete group of automorphisms of X of finite covolume. These "tree lattices" are the main object of study. Special attention is given to both parallels and contrasts with the case of Lie groups. Beyond the Lie group connection, the theory has application to combinatorics and number theory. The authors present a coherent survey of the results on uniform tree lattices, and a (previously unpublished) development of the theory of nonuniform tree lattices, including some fundamental and recently proved existence theorems. Nonuniform tree lattices are much more complicated than uniform ones; thus a good deal of attention is given to the construction and study of diverse examples. The fundamental technique is the encoding of tree action in terms of the corresponding quotient "graphs of groups." Tree Lattices should be a helpful resource to researcher sin the field, and may also be used for a graduate course on geometric methods in group theory
14 editions published between 2000 and 2001 in English and held by 307 WorldCat member libraries worldwide
Group actions on trees furnish a unified geometric way of recasting the chapter of combinatorial group theory dealing with free groups, amalgams, and HNN extensions. Some of the principal examples arise from rank one simple Lie groups over a nonarchimedean local field acting on their BruhatTits trees. In particular this leads to a powerful method for studying lattices in such Lie groups. This monograph extends this approach to the more general investigation of Xlattices G, where Xis a locally finite tree and G is a discrete group of automorphisms of X of finite covolume. These "tree lattices" are the main object of study. Special attention is given to both parallels and contrasts with the case of Lie groups. Beyond the Lie group connection, the theory has application to combinatorics and number theory. The authors present a coherent survey of the results on uniform tree lattices, and a (previously unpublished) development of the theory of nonuniform tree lattices, including some fundamental and recently proved existence theorems. Nonuniform tree lattices are much more complicated than uniform ones; thus a good deal of attention is given to the construction and study of diverse examples. The fundamental technique is the encoding of tree action in terms of the corresponding quotient "graphs of groups." Tree Lattices should be a helpful resource to researcher sin the field, and may also be used for a graduate course on geometric methods in group theory
Subgroup growth by
Alexander Lubotzky(
Book
)
16 editions published between 1993 and 2014 in English and held by 268 WorldCat member libraries worldwide
Subgroup growth studies the distribution of subgroups of finite index in a group as a function of the index. In the last two decades this topic has developed into one of the most active areas of research in infinite group theory; this book is a systematic and comprehensive account of the substantial theory which has emerged. As well as determining the range of possible "growth types", for finitely generated groups in general and for groups in particular classes such as linear groups, a main focus of the book is on the tight connection between the subgroup growth of a group and its algebraic structure. For example the socalled PSG Theorem, proved in Chapter 5, characterizes the groups of polynomial subgroup growth as those which are virtually soluble of finite rank. A key element in the proof is the growth of congruence subgroups in arithmetic groups, a new kind of "noncommutative arithmetic", with applications to the study of lattices in Lie groups. Another kind of noncommutative arithmetic arises with the introduction of subgroupcounting zeta functions; these fascinating and mysterious zeta functions have remarkable applications both to the "arithmetic of subgroup growth" and to the classification of finite pgroups. A wide range of mathematical disciplines play a significant role in this work: as well as various aspects of infinite group theory, these include finite simple groups and permutation groups, profinite groups, arithmetic groups and strong approximation, algebraic and analytic number theory, probability, and padic model theory. Relevant aspects of such topics are explained in selfcontained "windows", making the book accessible to a wide mathematical readership. The book concludes with over 60 challenging open problems that will stimulate further research in this rapidly growing subject
16 editions published between 1993 and 2014 in English and held by 268 WorldCat member libraries worldwide
Subgroup growth studies the distribution of subgroups of finite index in a group as a function of the index. In the last two decades this topic has developed into one of the most active areas of research in infinite group theory; this book is a systematic and comprehensive account of the substantial theory which has emerged. As well as determining the range of possible "growth types", for finitely generated groups in general and for groups in particular classes such as linear groups, a main focus of the book is on the tight connection between the subgroup growth of a group and its algebraic structure. For example the socalled PSG Theorem, proved in Chapter 5, characterizes the groups of polynomial subgroup growth as those which are virtually soluble of finite rank. A key element in the proof is the growth of congruence subgroups in arithmetic groups, a new kind of "noncommutative arithmetic", with applications to the study of lattices in Lie groups. Another kind of noncommutative arithmetic arises with the introduction of subgroupcounting zeta functions; these fascinating and mysterious zeta functions have remarkable applications both to the "arithmetic of subgroup growth" and to the classification of finite pgroups. A wide range of mathematical disciplines play a significant role in this work: as well as various aspects of infinite group theory, these include finite simple groups and permutation groups, profinite groups, arithmetic groups and strong approximation, algebraic and analytic number theory, probability, and padic model theory. Relevant aspects of such topics are explained in selfcontained "windows", making the book accessible to a wide mathematical readership. The book concludes with over 60 challenging open problems that will stimulate further research in this rapidly growing subject
Varieties of representations of finitely generated groups by
Alexander Lubotzky(
Book
)
14 editions published in 1985 in English and Italian and held by 237 WorldCat member libraries worldwide
14 editions published in 1985 in English and Italian and held by 237 WorldCat member libraries worldwide
Geometry, groups and dynamics : ICTS program, groups, geometry and dynamics, December 316, 2012, CEMS, Kumaun University,
Almora, India(
Book
)
2 editions published in 2015 in English and held by 8 WorldCat member libraries worldwide
"This volume contains the proceedings of the ICTS Program: Groups, Geometry and Dynamics, held December 316, 2012, at CEMS, Almora, India. The activity was an academic tribute to Ravi S. Kulkarni on his turning seventy. Articles included in this volume, both introductory and advanced surveys, represent the broad area of geometry that encompasses a large portion of group theory (finite or otherwise) and dynamics in its proximity. These areas have been influenced by Kulkarni's ideas and are closely related to his work and contribution."Page 4 of cover
2 editions published in 2015 in English and held by 8 WorldCat member libraries worldwide
"This volume contains the proceedings of the ICTS Program: Groups, Geometry and Dynamics, held December 316, 2012, at CEMS, Almora, India. The activity was an academic tribute to Ravi S. Kulkarni on his turning seventy. Articles included in this volume, both introductory and advanced surveys, represent the broad area of geometry that encompasses a large portion of group theory (finite or otherwise) and dynamics in its proximity. These areas have been influenced by Kulkarni's ideas and are closely related to his work and contribution."Page 4 of cover
The word and riemannian metrics on lattices of semisimple groups by
Alexander Lubotzky(
Book
)
1 edition published in 2000 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 2000 in English and held by 7 WorldCat member libraries worldwide
Scientific report : project: counting finite index subgroups and zeta function of groups ; grant no.: I071016.6/88, report
period: 19901993(
Book
)
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
Audience Level
0 

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Related Identities
 Bass, Hyman 1932 Author
 Segal, Daniel 1947
 Magid, Andy R. (Andy Roy) 1944
 Rogawski, Jonathan David Other Contributor
 Gongopadhyay, Krishnendu Editor
 Aravinda, C.S. Editor
 Goldman, William Mark (19......). Editor
 Mj, Mahan Editor
 Weaver, Anthony Editor
 Lo, Wu
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Associated Subjects
Algebra Algebraic varieties Combinatorial analysis Discrete groups Finite groups Geometry, Differential Geometry, NonEuclidean Global differential geometry Graph theory Group schemes (Mathematics) Group theory Hyperbolic spaces Infinite groups Invariant measures Lfunctions Lie groups Mathematics Number theory Representations of groups Subgroup growth (Mathematics) Topological groups Trees (Graph theory)
Alternative Names
Alexander Lubocky
Alexander Lubotzky
Alexander Lubotzky Israeli politician
Alexander Lubotzky israelischer Mathematiker und Politiker
Alexander Lubotzky wiskundige uit Israël
Lubotzky, A. 1956
אלכסנדר לובוצקי
アレクサンダー・ルボツキー
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