Borel, Armand
Overview
Works:  263 works in 989 publications in 6 languages and 13,406 library holdings 

Genres:  Conference papers and proceedings Biographies History 
Roles:  Author, Editor, Other, htt, Author of introduction, Contributor, Collector, Creator, Dedicatee, ed, Honoree 
Classifications:  QA3, 512.86 
Publication Timeline
.
Most widely held works about
Armand Borel
 Oeuvres = collected papers by Armand Borel( Book )
 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
)
52 editions published between 1969 and 2012 in 4 languages and held by 1,522 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
52 editions published between 1969 and 2012 in 4 languages and held by 1,522 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
Essays in the history of Lie groups and algebraic groups by
Armand Borel(
)
11 editions published in 2001 in English and held by 783 WorldCat member libraries worldwide
Annotation
11 editions published in 2001 in English and held by 783 WorldCat member libraries worldwide
Annotation
Seminar on transformation groups by
Armand Borel(
Book
)
19 editions published between 1960 and 2016 in 3 languages and held by 769 WorldCat member libraries worldwide
The book description for the forthcoming "Seminar on Transformation Groups. (AM46)" is not yet available
19 editions published between 1960 and 2016 in 3 languages and held by 769 WorldCat member libraries worldwide
The book description for the forthcoming "Seminar on Transformation Groups. (AM46)" is not yet available
Continuous cohomology, discrete subgroups, and representations of reductive groups by
Armand Borel(
Book
)
31 editions published between 1980 and 2014 in English and held by 759 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
31 editions published between 1980 and 2014 in English and held by 759 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
Almost commuting elements in compact Lie groups by
Armand Borel(
)
13 editions published between 2002 and 2012 in English and held by 727 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
13 editions published between 2002 and 2012 in English and held by 727 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
Seminar on algebraic groups and related finite groups, held at the Institute for Advanced Study, Princeton/NJ, 1968/69 by
A Borel(
Book
)
53 editions published between 1970 and 2006 in 5 languages and held by 715 WorldCat member libraries worldwide
53 editions published between 1970 and 2006 in 5 languages and held by 715 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
)
41 editions published between 1951 and 2007 in 3 languages and held by 682 WorldCat member libraries worldwide
41 editions published between 1951 and 2007 in 3 languages and held by 682 WorldCat member libraries worldwide
Compactifications of symmetric and locally symmetric spaces by
Armand Borel(
)
25 editions published between 2006 and 2008 in English and held by 675 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
25 editions published between 2006 and 2008 in English and held by 675 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
Topics in the homology theory of fibre bundles; lectures given at the University of Chicago, 1954 by
Armand Borel(
Book
)
23 editions published between 1967 and 2006 in English and German and held by 664 WorldCat member libraries worldwide
23 editions published between 1967 and 2006 in English and German and held by 664 WorldCat member libraries worldwide
Seminar on complex multiplication by
Armand Borel(
Book
)
42 editions published between 1966 and 1989 in 4 languages and held by 637 WorldCat member libraries worldwide
42 editions published between 1966 and 1989 in 4 languages and held by 637 WorldCat member libraries worldwide
Représentations de groupes localement compacts by
Armand Borel(
Book
)
21 editions published between 1962 and 1972 in French and German and held by 601 WorldCat member libraries worldwide
21 editions published between 1962 and 1972 in French and German and held by 601 WorldCat member libraries worldwide
Automorphic forms, representations, and Lfunctions by
Armand Borel(
Book
)
42 editions published between 1977 and 2012 in English and held by 506 WorldCat member libraries worldwide
42 editions published between 1977 and 2012 in English and held by 506 WorldCat member libraries worldwide
Algebraic groups and discontinuous subgroups by
American Mathematical Society(
Book
)
33 editions published between 1963 and 2012 in English and Undetermined and held by 461 WorldCat member libraries worldwide
33 editions published between 1963 and 2012 in English and Undetermined and held by 461 WorldCat member libraries worldwide
Intersection cohomology by
Armand Borel(
Book
)
28 editions published between 1984 and 2008 in 3 languages and held by 441 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
28 editions published between 1984 and 2008 in 3 languages and held by 441 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
Introduction aux groupes arithmétiques by
Armand Borel(
Book
)
23 editions published between 1920 and 2019 in French and English and held by 406 WorldCat member libraries worldwide
Some classical groups  Algebraic groups  Fundamental sets with cusps
23 editions published between 1920 and 2019 in French and English and held by 406 WorldCat member libraries worldwide
Some classical groups  Algebraic groups  Fundamental sets with cusps
Hermann Weyl, 18851985 : centenary lectures by
Chen Ning Yang(
Book
)
14 editions published in 1986 in English and held by 384 WorldCat member libraries worldwide
14 editions published in 1986 in English and held by 384 WorldCat member libraries worldwide
Automorphic forms on SL₂(R) by
Armand Borel(
Book
)
20 editions published between 1997 and 2011 in English and Undetermined and held by 381 WorldCat member libraries worldwide
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, used only for G and its analytic subgroups
20 editions published between 1997 and 2011 in English and Undetermined and held by 381 WorldCat member libraries worldwide
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, used only for G and its analytic subgroups
Algebraic Dmodules by
Armand Borel(
Book
)
14 editions published between 1987 and 1988 in English and Undetermined and held by 326 WorldCat member libraries worldwide
14 editions published between 1987 and 1988 in English and Undetermined and held by 326 WorldCat member libraries worldwide
Semisimple groups and Riemannian symmetric spaces by
Armand Borel(
Book
)
11 editions published between 1998 and 2011 in English and held by 172 WorldCat member libraries worldwide
11 editions published between 1998 and 2011 in English and held by 172 WorldCat member libraries worldwide
Oeuvres = collected papers by
Armand Borel(
Book
)
28 editions published between 1958 and 2015 in 4 languages and held by 121 WorldCat member libraries worldwide
Armand Borel’s mathematical work centered on the theory of Lie groups. Because of the increasingly important place of this theory in the whole of mathematics, Borel’s work influenced some of the most important developments of contemporary mathematics. His first great achievement was to apply to Lie groups and homogenous spaces the powerful techniques of algebraic topology developed by Leray, Cartan, and Steenrod. In 1992, Borel was awarded the International Balzan Prize for Mathematics "for his fundamental contributions to the theory of Lie groups, algebraic groups and arithmetic groups, and for his indefatigable action in favor of high quality in mathematical research and of the propagation of new ideas." He wrote more than 145 articles before 1982, which were collected in three volumes published in 1983. A fourth volume of subsequent articles was published in 2001. Volume I collects the papers written from 1948 to 1958
28 editions published between 1958 and 2015 in 4 languages and held by 121 WorldCat member libraries worldwide
Armand Borel’s mathematical work centered on the theory of Lie groups. Because of the increasingly important place of this theory in the whole of mathematics, Borel’s work influenced some of the most important developments of contemporary mathematics. His first great achievement was to apply to Lie groups and homogenous spaces the powerful techniques of algebraic topology developed by Leray, Cartan, and Steenrod. In 1992, Borel was awarded the International Balzan Prize for Mathematics "for his fundamental contributions to the theory of Lie groups, algebraic groups and arithmetic groups, and for his indefatigable action in favor of high quality in mathematical research and of the propagation of new ideas." He wrote more than 145 articles before 1982, which were collected in three volumes published in 1983. A fourth volume of subsequent articles was published in 2001. Volume I collects the papers written from 1948 to 1958
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Related Identities
 Institute for Advanced Study (Princeton, N.J.) Other
 American Mathematical Society Publisher Organizer of meeting Editor
 Wallach, Nolan R. Contributor
 Morgan, John 1946 March 21
 Friedman, Robert 1955
 Ji, Lizhen 1964 Translator Editor
 Casselman, Bill 1941 Other Editor
 Mostow, George D. Editor
 Bass, Hyman 1932 Compiler Editor
 Yang, Chen Ning 1922 Author
Useful Links
Associated Subjects
Algebra Algebraic number theory Algebraic topology Automorphic forms Awards Borel, Armand Canada Class field theory Compact groups Compactifications Continuous groups Differentiable manifolds Dmodules Fiber bundles (Mathematics) Finite groups Finite simple groups Geometry Germany Germs (Mathematics) Group theory Homology theory Intersection homology theory Intersection theory (Mathematics) Leray, Jean, Lfunctions Lie algebras Lie groups Linear algebraic groups Locally compact groups Locally compact spaces Mathematical physics Mathematicians Mathematics Medals Modules (Algebra) Multiplication, Complex Numbers, Complex Number theory Piecewise linear topology Representations of groups Riemannian manifolds Rings (Algebra) Root systems (Algebra) Semisimple Lie groups Set theory Sheaf theory Symmetric spaces Topology Transformation groups Weyl, Hermann,
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Alternative Names
Armand Borel matamaiticeoir Eilvéiseach
Armand Borel matemàtic suís
Armand Borel matemático suizo
Armand Borel matematico svizzero
Armand Borel matematikan zviceran
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 Swiss mathematician (19232003)
Armand Borel Zwitsers wiskundige
Borel A.
Borel, A. 19232003
Borel, A. (Armand)
Borel, A. (Armand), 19232003
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