Borel, Armand
Overview
Works:  177 works in 849 publications in 5 languages and 11,026 library holdings 

Genres:  Conference papers and proceedings Biography History 
Roles:  Author, Editor, Contributor, Author of introduction, Other, Creator, Dedicatee, Honoree, ed 
Classifications:  QA3, 512.86 
Publication Timeline
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Most widely held works about
Armand Borel
 Borel, Armand : Mathematics( )
 Armand Borel : 21 May 192311 August 2003 by Enrico Bombieri( Book )
Most widely held works by
Armand Borel
Linear algebraic groups by
Armand Borel(
Book
)
47 editions published between 1969 and 2012 in 4 languages and held by 1,034 WorldCat member libraries worldwide
This book is a revised and enlarged edition of "Linear Algebraic Groups", published by W.A. Benjamin in 1969. The text of the first edition has been corrected and revised. Accordingly, this book presents foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces. After establishing these basic topics, the text then turns to solvable groups, general properties of linear algebraic groups and Chevally's structure theory of reductive groups over algebraically closed groundfields. The remainder of the book is devoted to rationality questions over nonalgebraically closed fields. This second edition has been expanded to include material on central isogenies and the structure of the group of rational points of an isotropic reductive group. The main prerequisite is some familiarity with algebraic geometry. The main notions and results needed are summarized in a chapter with references and brief proofs
47 editions published between 1969 and 2012 in 4 languages and held by 1,034 WorldCat member libraries worldwide
This book is a revised and enlarged edition of "Linear Algebraic Groups", published by W.A. Benjamin in 1969. The text of the first edition has been corrected and revised. Accordingly, this book presents foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces. After establishing these basic topics, the text then turns to solvable groups, general properties of linear algebraic groups and Chevally's structure theory of reductive groups over algebraically closed groundfields. The remainder of the book is devoted to rationality questions over nonalgebraically closed fields. This second edition has been expanded to include material on central isogenies and the structure of the group of rational points of an isotropic reductive group. The main prerequisite is some familiarity with algebraic geometry. The main notions and results needed are summarized in a chapter with references and brief proofs
Seminar on transformation groups by
Armand Borel(
Book
)
31 editions published between 1960 and 2016 in English and Italian and held by 695 WorldCat member libraries worldwide
The book description for the forthcoming "Seminar on Transformation Groups. (AM46)" is not yet available
31 editions published between 1960 and 2016 in English and Italian and held by 695 WorldCat member libraries worldwide
The book description for the forthcoming "Seminar on Transformation Groups. (AM46)" is not yet available
Seminar on algebraic groups and related finite groups, held at the Institute for Advanced Study, Princeton/NJ, 1968/69 by
Armand Borel(
Book
)
51 editions published between 1970 and 2008 in 5 languages and held by 656 WorldCat member libraries worldwide
51 editions published between 1970 and 2008 in 5 languages and held by 656 WorldCat member libraries worldwide
Topics in the homology theory of fibre bundles; lectures given at the University of Chicago, 1954 by
Armand Borel(
Book
)
36 editions published in 1967 in English and German and held by 644 WorldCat member libraries worldwide
36 editions published in 1967 in English and German and held by 644 WorldCat member libraries worldwide
Compactifications of symmetric and locally symmetric spaces by
Armand Borel(
)
23 editions published between 2006 and 2008 in English and held by 639 WorldCat member libraries worldwide
Noncompact symmetric and locally symmetric spaces naturally appear in many mathematical theories, including analysis (representation theory, nonabelian harmonic analysis), number theory (automorphic forms), algebraic geometry (modulae) and algebraic topology (cohomology of discrete groups). In most applications it is necessary to form an appropriate compactification of the space. The literature dealing with such compactifications is vast. The main purpose of this book is to introduce uniform constructions of most of the known compactifications with emphasis on their geometric and topological structures. The book is divided into three parts. Part I studies compactifications of Riemannian symmetric spaces and their arithmetic quotients. Part II is a study of compact smooth manifolds. Part III studies the compactification of locally symmetric spaces. Familiarity with the theory of semisimple Lie groups is assumed, as is familiarity with algebraic groups defined over the rational numbers in later parts of the book, although most of the pertinent material is recalled as presented. Otherwise, the book is a selfcontained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to diverse fields of mathematics
23 editions published between 2006 and 2008 in English and held by 639 WorldCat member libraries worldwide
Noncompact symmetric and locally symmetric spaces naturally appear in many mathematical theories, including analysis (representation theory, nonabelian harmonic analysis), number theory (automorphic forms), algebraic geometry (modulae) and algebraic topology (cohomology of discrete groups). In most applications it is necessary to form an appropriate compactification of the space. The literature dealing with such compactifications is vast. The main purpose of this book is to introduce uniform constructions of most of the known compactifications with emphasis on their geometric and topological structures. The book is divided into three parts. Part I studies compactifications of Riemannian symmetric spaces and their arithmetic quotients. Part II is a study of compact smooth manifolds. Part III studies the compactification of locally symmetric spaces. Familiarity with the theory of semisimple Lie groups is assumed, as is familiarity with algebraic groups defined over the rational numbers in later parts of the book, although most of the pertinent material is recalled as presented. Otherwise, the book is a selfcontained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to diverse fields of mathematics
Seminar on complex multiplication by
Armand Borel(
Book
)
44 editions published between 1966 and 1989 in 4 languages and held by 627 WorldCat member libraries worldwide
44 editions published between 1966 and 1989 in 4 languages and held by 627 WorldCat member libraries worldwide
Représentations de groupes localement compacts by
Armand Borel(
Book
)
25 editions published between 1962 and 1972 in 4 languages and held by 582 WorldCat member libraries worldwide
25 editions published between 1962 and 1972 in 4 languages and held by 582 WorldCat member libraries worldwide
Cohomologie des espaces localement compacts d'après J. Leray : exposés faits au Séminaire de topologie algébrique de l'École
polytechnique fédérale au printemps 1951 by
Armand Borel(
Book
)
39 editions published between 1964 and 2007 in 3 languages and held by 571 WorldCat member libraries worldwide
39 editions published between 1964 and 2007 in 3 languages and held by 571 WorldCat member libraries worldwide
Automorphic forms, representations, and Lfunctions by
Armand Borel(
Book
)
47 editions published between 1977 and 2012 in English and held by 499 WorldCat member libraries worldwide
47 editions published between 1977 and 2012 in English and held by 499 WorldCat member libraries worldwide
Algebraic groups and discontinuous subgroups by Symposium in Pure Mathematics(
Book
)
29 editions published between 1963 and 2012 in English and Undetermined and held by 450 WorldCat member libraries worldwide
29 editions published between 1963 and 2012 in English and Undetermined and held by 450 WorldCat member libraries worldwide
Continuous cohomology, discrete subgroups, and representations of reductive groups by
Armand Borel(
Book
)
16 editions published in 1980 in English and held by 434 WorldCat member libraries worldwide
It has been nearly twenty years since the first edition of this work. In the intervening years, there has been immense progress in the use of homological algebra to construct admissible representations and in the study of arithmetic groups. This second edition is a corrected and expanded version of the original, which was an important catalyst in the expansion of the field. Besides the fundamental material on cohomology and discrete subgroups present in the first edition, this edition also contains expositions of some of the most important developments of the last two decades
16 editions published in 1980 in English and held by 434 WorldCat member libraries worldwide
It has been nearly twenty years since the first edition of this work. In the intervening years, there has been immense progress in the use of homological algebra to construct admissible representations and in the study of arithmetic groups. This second edition is a corrected and expanded version of the original, which was an important catalyst in the expansion of the field. Besides the fundamental material on cohomology and discrete subgroups present in the first edition, this edition also contains expositions of some of the most important developments of the last two decades
Intersection cohomology by
Armand Borel(
Book
)
25 editions published between 1984 and 2008 in English and Undetermined and held by 405 WorldCat member libraries worldwide
This book is a publication in Swiss Seminars, a subseries of Progress in Mathematics. It is an expanded version of the notes from a seminar on intersection cohomology theory, which met at the University of Bern, Switzerland, in the spring of 1983. This volume supplies an introduction to the piecewise linear and sheaftheoretic versions of that theory as developed by M. Goresky and R. MacPherson in Topology 19 (1980), and in Inventiones Mathematicae 72 (1983). While some familiarity with algebraic topology and sheaf theory is assumed, the notes include a selfcontained account of further material on constructibility, derived categories, Verdier duality, biduality, and on stratified spaces, which is used in the second paper but not found in standard texts. "The volume should be useful to someone interested in acquiring some basic knowledge about the field ..." Mathematical Reviews
25 editions published between 1984 and 2008 in English and Undetermined and held by 405 WorldCat member libraries worldwide
This book is a publication in Swiss Seminars, a subseries of Progress in Mathematics. It is an expanded version of the notes from a seminar on intersection cohomology theory, which met at the University of Bern, Switzerland, in the spring of 1983. This volume supplies an introduction to the piecewise linear and sheaftheoretic versions of that theory as developed by M. Goresky and R. MacPherson in Topology 19 (1980), and in Inventiones Mathematicae 72 (1983). While some familiarity with algebraic topology and sheaf theory is assumed, the notes include a selfcontained account of further material on constructibility, derived categories, Verdier duality, biduality, and on stratified spaces, which is used in the second paper but not found in standard texts. "The volume should be useful to someone interested in acquiring some basic knowledge about the field ..." Mathematical Reviews
Hermann Weyl, 18851985 : centenary lectures by
Chen Ning Yang(
Book
)
13 editions published in 1986 in English and held by 378 WorldCat member libraries worldwide
13 editions published in 1986 in English and held by 378 WorldCat member libraries worldwide
Automorphic forms on SL₂(R) by
Armand Borel(
Book
)
18 editions published between 1997 and 2008 in English and Undetermined and held by 358 WorldCat member libraries worldwide
This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upperhalf plane X, with respect to a discrete subgroup G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making this connection explicit. The topics treated include the construction of fundamental domains, the notion of automorphic form on G\"G and its relationship with the classical automorphic forms on X, Poincare series, constant terms, cusp forms, finite dimensionality of the space of automorphic forms of a given type, compactness of certain convolution operators, Eisenstein series, unitary representations of G, and the spectral decomposition of L2 (G\"G). The main prerequisites are some results in functional analysis (reviewed, with references) and some familiarity with the elementary theory of Lie groups and Lie algebras. Graduate students and researchers in analytic number theory will find much to interest them in this book
18 editions published between 1997 and 2008 in English and Undetermined and held by 358 WorldCat member libraries worldwide
This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upperhalf plane X, with respect to a discrete subgroup G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making this connection explicit. The topics treated include the construction of fundamental domains, the notion of automorphic form on G\"G and its relationship with the classical automorphic forms on X, Poincare series, constant terms, cusp forms, finite dimensionality of the space of automorphic forms of a given type, compactness of certain convolution operators, Eisenstein series, unitary representations of G, and the spectral decomposition of L2 (G\"G). The main prerequisites are some results in functional analysis (reviewed, with references) and some familiarity with the elementary theory of Lie groups and Lie algebras. Graduate students and researchers in analytic number theory will find much to interest them in this book
Continuous cohomology, discrete subgroups, and representations of reductive groups by
Armand Borel(
Book
)
16 editions published between 1999 and 2014 in English and held by 353 WorldCat member libraries worldwide
16 editions published between 1999 and 2014 in English and held by 353 WorldCat member libraries worldwide
Essays in the history of Lie groups and algebraic groups by
Armand Borel(
Book
)
10 editions published in 2001 in English and held by 327 WorldCat member libraries worldwide
Lie groups and algebraic groups are important in many major areas of mathematics and mathematical physics. We find them in diverse roles, notably as groups of automorphisms of geometric structures, as symmetries of differential systems, or as basic tools in the theory of automorphic forms. The author looks at their development, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. Starting from Lie's theory of local analytic transformation groups and early work on Lie algebras, he follows the process of globalization in its two mai
10 editions published in 2001 in English and held by 327 WorldCat member libraries worldwide
Lie groups and algebraic groups are important in many major areas of mathematics and mathematical physics. We find them in diverse roles, notably as groups of automorphisms of geometric structures, as symmetries of differential systems, or as basic tools in the theory of automorphic forms. The author looks at their development, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. Starting from Lie's theory of local analytic transformation groups and early work on Lie algebras, he follows the process of globalization in its two mai
Algebraic Dmodules by
Armand Borel(
Book
)
14 editions published between 1987 and 1988 in English and Undetermined and held by 317 WorldCat member libraries worldwide
14 editions published between 1987 and 1988 in English and Undetermined and held by 317 WorldCat member libraries worldwide
Oeuvres = collected papers by
Armand Borel(
Book
)
24 editions published between 1983 and 2013 in English and French and held by 309 WorldCat member libraries worldwide
24 editions published between 1983 and 2013 in English and French and held by 309 WorldCat member libraries worldwide
Introduction aux groupes arithmétiques by
Armand Borel(
Book
)
17 editions published between 1965 and 1984 in French and English and held by 289 WorldCat member libraries worldwide
17 editions published between 1965 and 1984 in French and English and held by 289 WorldCat member libraries worldwide
Almost commuting elements in compact Lie groups by
Armand Borel(
Book
)
12 editions published in 2002 in English and held by 273 WorldCat member libraries worldwide
Introduction Almost commuting $N$tuples Some characterizations of groups of type $A$ $c$pairs Commuting triples Some results on diagram automorphisms and associated root systems The fixed subgroup of an automorphism $C$triples The tori $\overline{S}(k)$ and $\overline{S}^{w_c}(\overline{\bf g}, k)$ and their Weyl groups The ChernSimons invariant The case when $\langle C\rangle$ is not cyclic Bibliography Diagrams and tables
12 editions published in 2002 in English and held by 273 WorldCat member libraries worldwide
Introduction Almost commuting $N$tuples Some characterizations of groups of type $A$ $c$pairs Commuting triples Some results on diagram automorphisms and associated root systems The fixed subgroup of an automorphism $C$triples The tori $\overline{S}(k)$ and $\overline{S}^{w_c}(\overline{\bf g}, k)$ and their Weyl groups The ChernSimons invariant The case when $\langle C\rangle$ is not cyclic Bibliography Diagrams and tables
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Related Identities
 Institute for Advanced Study (Princeton, N.J.)
 American Mathematical Society Publisher Editor
 Wallach, Nolan R. Contributor
 Ji, Lizhen 1964
 Casselman, Bill 1941 Editor
 Mostow, George D. Editor
 Bass, Hyman 1932 Compiler
 Chandrasekharan, K. (Komaravolu) 1920 Editor
 Yang, Chen Ning 1922 Author Contributor
 Penrose, Roger Contributor
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Associated Subjects
Algebra Algebraic topology Arithmetic groups Automorphic forms Awards Canada Class field theory College teachers Compact groups Compactifications Differentiable manifolds Dmodules Fiber bundles (Mathematics) Finite groups Finite simple groups Geometry Geometry, Algebraic Germany Germs (Mathematics) Group theory Homology theory Intersection homology theory Intersection theory (Mathematics) Lecturers Lfunctions Lie groups Linear algebraic groups Locally compact groups Mathematical physics Mathematicians Mathematics Medals Modules (Algebra) Multiplication, Complex Numbers, Complex Number theory Piecewise linear topology Representations of groups Research Rings (Algebra) Root systems (Algebra) Scientists Set theory Sheaf theory Symmetric spaces Topological groups Transformation groups Transformations (Mathematics) United States Weyl, Hermann,
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Alternative Names
Armand Borel matemàtic suís
Armand Borel matemático suizo
Armand Borel matematico svizzero
Armand Borel Schweizer Mathematiker
Armand Borel schweizisk matematiker
Armand Borel svájci matematikus, topológus
Armand Borel sveitsisk matematikar
Armand Borel sveitsisk matematiker
Armand Borel Svisa matematikisto
Armand Borel švýcarský matematik
Armand Borel Swiss mathematician
Armand Borel Zwitsers wiskundige
Borel, A.
Borel, A. 19232003
Borel, A. (Armand)
Borel, Armand
Borelʹ, Armand 19232003
Арман Барэль
Арман Борель
Борель, А..
أرمان بورل
أرمان بورل رياضياتي سويسري
آرمند بورل ریاضیدان سوئیسی
아르망 보렐
アルマン・ボレル
阿爾芒·博雷尔
Languages