WorldCat Identities

Borel, Armand

Overview
Works: 170 works in 837 publications in 5 languages and 10,930 library holdings
Genres: Conference papers and proceedings  Biography  History 
Roles: Author, Editor, Contributor, Author of introduction, Other, Creator, Honoree, ed, Dedicatee
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 )

47 editions published between 1969 and 2012 in 4 languages and held by 1,040 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
Seminar on transformation groups by Armand Borel( Book )

32 editions published between 1960 and 2016 in 3 languages and held by 683 WorldCat member libraries worldwide

The book description for the forthcoming "Seminar on Transformation Groups. (AM-46)" is not yet available
Compactifications of symmetric and locally symmetric spaces by Armand Borel( )

23 editions published between 2006 and 2008 in English and held by 640 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
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 633 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 620 WorldCat member libraries worldwide

Seminar on complex multiplication by Armand Borel( Book )

44 editions published between 1966 and 1989 in 4 languages and held by 602 WorldCat member libraries worldwide

Représentations de groupes localement compacts by Armand Borel( Book )

26 editions published between 1962 and 1972 in 4 languages and held by 559 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 )

40 editions published between 1964 and 2007 in 3 languages and held by 540 WorldCat member libraries worldwide

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

44 editions published between 1979 and 2004 in English and Undetermined and held by 504 WorldCat member libraries worldwide

Algebraic groups and discontinuous subgroups by Symposium in Pure Mathematics of American Mathematical Society( Book )

28 editions published between 1963 and 2004 in English and Undetermined and held by 457 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 437 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 407 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
Hermann Weyl, 1885-1985 : centenary lectures by Chen Ning Yang( Book )

13 editions published in 1986 in English and held by 380 WorldCat member libraries worldwide

Automorphic forms on SL₂(R) by Armand Borel( Book )

17 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 upper-half 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 )

15 editions published between 1999 and 2014 in English and held by 355 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 328 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 D-modules by Armand Borel( Book )

14 editions published between 1987 and 1988 in English and Undetermined and held by 320 WorldCat member libraries worldwide

Oeuvres = collected papers by Armand Borel( Book )

23 editions published between 1983 and 2013 in English and French and held by 310 WorldCat member libraries worldwide

Introduction aux groupes arithmétiques by Armand Borel( Book )

16 editions published between 1969 and 1984 in French and English and held by 295 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 275 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
 
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Compactifications of symmetric and locally symmetric spaces
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 Swiss mathematician

Armand Borel Zwitsers wiskundige

Borel, A.

Borel, A. 1923-2003

Borel, A. (Armand)

Borel, Armand

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
English (421)

French (66)

German (17)

Russian (8)

Italian (2)

Covers
Seminar on transformation groupsCompactifications of symmetric and locally symmetric spacesSeminar on algebraic groups and related finite groups, held at the Institute for Advanced Study, Princeton/NJ, 1968/69Seminar on complex multiplicationReprésentations de groupes localement compactsCohomologie des espaces localement compacts d'après J. Leray : exposés faits au Séminaire de topologie algébrique de l'École polytechnique fédérale au printemps 1951Continuous cohomology, discrete subgroups, and representations of reductive groupsIntersection cohomology