WorldCat Identities

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
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Most widely held works about Armand Borel
 
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 non-algebraically 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
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. (AM-46)" 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
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 Chern-Simons 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

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

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 self-contained 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

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

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

Automorphic forms, representations, and L-functions by Armand Borel( Book )

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

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 sheaf-theoretic 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 self-contained 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
Hermann Weyl, 1885-1985 : centenary lectures by Chen Ning Yang( Book )

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
Algebraic D-modules by Armand Borel( Book )

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

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
 
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Compactifications of symmetric and locally symmetric spaces
Covers
Essays in the history of Lie groups and algebraic groupsSeminar on transformation groupsContinuous cohomology, discrete subgroups, and representations of reductive groupsAlmost commuting elements in compact Lie groupsSeminar on algebraic groups and related finite groups, held at the Institute for Advanced Study, Princeton/NJ, 1968/69Cohomologie des espaces localement compacts d'après J. Leray : exposés faits au Séminaire de topologie algébrique de l'École polytechnique fédérale au printemps 1951Compactifications of symmetric and locally symmetric spacesTopics in the homology theory of fibre bundles; lectures given at the University of Chicago, 1954
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 (1923-2003)

Armand Borel Zwitsers wiskundige

Borel A.

Borel, A. 1923-2003

Borel, A. (Armand)

Borel, A. (Armand), 1923-2003

Borelʹ, Armand 1923-2003

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