Gabriel, Peter 1933
Overview
Works:  53 works in 392 publications in 8 languages and 5,465 library holdings 

Genres:  Conference papers and proceedings History 
Roles:  Author, Editor, Redactor, Collector, Other 
Classifications:  QA3, 513.83 
Publication Timeline
.
Most widely held works by
Peter Gabriel
Calculus of fractions and homotopy theory by
Peter Gabriel(
Book
)
24 editions published in 1967 in 3 languages and held by 543 WorldCat member libraries worldwide
The main purpose of the present work is to present to the reader a particularly nice category for the study of homotopy, namely the homo topic category (IV). This category is, in fact,  according to Chapter VII and a wellknown theorem of J.H.C. WHITEHEAD  equivalent to the category of CWcomplexes modulo homotopy, i.e. the category whose objects are spaces of the homotopy type of a CWcomplex and whose morphisms are homotopy classes of continuous mappings between such spaces. It is also equivalent (I, 1.3) to a category of fractions of the category of topological spaces modulo homotopy, and to the category of Kan complexes modulo homotopy (IV). In order to define our homotopic category, it appears useful to follow as closely as possible methods which have proved efficacious in homo logical algebra. Our category is thus the" topological" analogue of the derived category of an abelian category (VERDIER). The algebraic machinery upon which this work is essentially based includes the usual grounding in category theory  summarized in the Dictionary  and the theory of categories of fractions which forms the subject of the first chapter of the book. The merely topological machinery reduces to a few properties of Kelley spaces (Chapters I and III). The starting point of our study is the category,10 Iff of simplicial sets (C.S.S. complexes or semisimplicial sets in a former terminology)
24 editions published in 1967 in 3 languages and held by 543 WorldCat member libraries worldwide
The main purpose of the present work is to present to the reader a particularly nice category for the study of homotopy, namely the homo topic category (IV). This category is, in fact,  according to Chapter VII and a wellknown theorem of J.H.C. WHITEHEAD  equivalent to the category of CWcomplexes modulo homotopy, i.e. the category whose objects are spaces of the homotopy type of a CWcomplex and whose morphisms are homotopy classes of continuous mappings between such spaces. It is also equivalent (I, 1.3) to a category of fractions of the category of topological spaces modulo homotopy, and to the category of Kan complexes modulo homotopy (IV). In order to define our homotopic category, it appears useful to follow as closely as possible methods which have proved efficacious in homo logical algebra. Our category is thus the" topological" analogue of the derived category of an abelian category (VERDIER). The algebraic machinery upon which this work is essentially based includes the usual grounding in category theory  summarized in the Dictionary  and the theory of categories of fractions which forms the subject of the first chapter of the book. The merely topological machinery reduces to a few properties of Kelley spaces (Chapters I and III). The starting point of our study is the category,10 Iff of simplicial sets (C.S.S. complexes or semisimplicial sets in a former terminology)
Representation theory : proceedings of the Workshop on the Present Trends in Representation Theory, Ottawa, Carleton University,
August 1328, 1979 by
Vlastimil Dlab(
Book
)
54 editions published between 1980 and 1986 in English and German and held by 449 WorldCat member libraries worldwide
54 editions published between 1980 and 1986 in English and German and held by 449 WorldCat member libraries worldwide
Representations of algebras : proceedings of the international conference, Ottawa 1974 by
Vlastimil Dlab(
Book
)
20 editions published between 1974 and 1975 in English and German and held by 401 WorldCat member libraries worldwide
20 editions published between 1974 and 1975 in English and German and held by 401 WorldCat member libraries worldwide
Lokal präsentierbare Kategorien by
Peter Gabriel(
Book
)
26 editions published between 1971 and 2008 in 4 languages and held by 394 WorldCat member libraries worldwide
26 editions published between 1971 and 2008 in 4 languages and held by 394 WorldCat member libraries worldwide
Primideale in Einhüllenden auflösbarer LieAlgebren. Beschreibung durch Bahnenräume by
W Borho(
Book
)
26 editions published between 1973 and 2008 in 5 languages and held by 393 WorldCat member libraries worldwide
26 editions published between 1973 and 2008 in 5 languages and held by 393 WorldCat member libraries worldwide
Algèbre locale, multiplicités; cours au Collège de France, 19571958 by
JeanPierre Serre(
Book
)
44 editions published between 1958 and 2002 in 4 languages and held by 381 WorldCat member libraries worldwide
This edition reproduces the 2nd corrected printing of the 3rd edition of the now classic notes by Professor Serre, long established as one of the standard introductory texts on local algebra. Referring for background notions to Bourbaki's "Commutative Algebra" (English edition SpringerVerlag 1988), the book focusses on the various dimension theories and theorems on mulitplicities of intersections with the CartanEilenberg functor Tor as the central concept. The main results are the decomposition theorems, theorems of CohenSeidenberg, the normalisation of rings of polynomials, dimension (in the sense of Krull) and characteristic polynomials (in the sense of HilbertSamuel)
44 editions published between 1958 and 2002 in 4 languages and held by 381 WorldCat member libraries worldwide
This edition reproduces the 2nd corrected printing of the 3rd edition of the now classic notes by Professor Serre, long established as one of the standard introductory texts on local algebra. Referring for background notions to Bourbaki's "Commutative Algebra" (English edition SpringerVerlag 1988), the book focusses on the various dimension theories and theorems on mulitplicities of intersections with the CartanEilenberg functor Tor as the central concept. The main results are the decomposition theorems, theorems of CohenSeidenberg, the normalisation of rings of polynomials, dimension (in the sense of Krull) and characteristic polynomials (in the sense of HilbertSamuel)
Representation theory II : proceedings of the Second International Conference on Representations of Algebras, Ottawa, Carleton
University, August 1325, 1979 by
Vlastimil Dlab(
Book
)
34 editions published in 1980 in English and German and held by 327 WorldCat member libraries worldwide
34 editions published in 1980 in English and German and held by 327 WorldCat member libraries worldwide
Groupes algébriques by
Michel Demazure(
Book
)
31 editions published in 1970 in 4 languages and held by 294 WorldCat member libraries worldwide
31 editions published in 1970 in 4 languages and held by 294 WorldCat member libraries worldwide
Introduction to algebraic geometry and algebraic groups by
Michel Demazure(
Book
)
20 editions published in 1980 in English and Dutch and held by 287 WorldCat member libraries worldwide
20 editions published in 1980 in English and Dutch and held by 287 WorldCat member libraries worldwide
Matrices, géométrie, algèbre linéaire by
Peter Gabriel(
Book
)
19 editions published between 1996 and 2001 in 3 languages and held by 234 WorldCat member libraries worldwide
Der heutige Hochschulunterricht für Mathematiker gründet meist auf Abstraktion und führt vom Allgemeinen zum Speziellen. Die Methode hat Vorteile, sie stärkt das Denkvermögen und meidet lästige Wiederholungen. Doch sie "stellt den Pflug vor die Ochsen", weil Abstraktion auf Spezialfälle baut, die dem Lernenden oft fremd sind. So bleibt der Erfolg den Glücklichen vorbehalten, die den Weg von der Abstraktion zu den Beispielen finden. Dieses Lehrbuch führt von zwei Spezialfällen zur Allgemeinheit und gründet nicht auf Abstraktion. Die Beweise der abstrakten Algebra werden zuerst am konkreten Beispiel der Matrizen vorgeführt. Zur Schärfung der Anschauung wird dann die Begriffswelt der Elementargeometrie durchleuchtet. Die Auseinandersetzung mit dem Lehrstoff der Schule dient der Vorbereitung auf die geometrisch gefärbte Sprache der linearen Algebra, die am Ende des Buches erläutert wird. Dem Text sind Anwendungsbeispiele und zahlreiche historische Kommentare beigefügt
19 editions published between 1996 and 2001 in 3 languages and held by 234 WorldCat member libraries worldwide
Der heutige Hochschulunterricht für Mathematiker gründet meist auf Abstraktion und führt vom Allgemeinen zum Speziellen. Die Methode hat Vorteile, sie stärkt das Denkvermögen und meidet lästige Wiederholungen. Doch sie "stellt den Pflug vor die Ochsen", weil Abstraktion auf Spezialfälle baut, die dem Lernenden oft fremd sind. So bleibt der Erfolg den Glücklichen vorbehalten, die den Weg von der Abstraktion zu den Beispielen finden. Dieses Lehrbuch führt von zwei Spezialfällen zur Allgemeinheit und gründet nicht auf Abstraktion. Die Beweise der abstrakten Algebra werden zuerst am konkreten Beispiel der Matrizen vorgeführt. Zur Schärfung der Anschauung wird dann die Begriffswelt der Elementargeometrie durchleuchtet. Die Auseinandersetzung mit dem Lehrstoff der Schule dient der Vorbereitung auf die geometrisch gefärbte Sprache der linearen Algebra, die am Ende des Buches erläutert wird. Dem Text sind Anwendungsbeispiele und zahlreiche historische Kommentare beigefügt
Proceedings of the Fourth International Conference on Representations of Algebras held in Ottawa, Canada, August 1625, 1984 by International Conference on Representations of Algebras(
Book
)
5 editions published in 1986 in English and held by 189 WorldCat member libraries worldwide
5 editions published in 1986 in English and held by 189 WorldCat member libraries worldwide
Representations of finitedimensional algebras by
Peter Gabriel(
Book
)
1 edition published in 1997 in English and held by 147 WorldCat member libraries worldwide
1 edition published in 1997 in English and held by 147 WorldCat member libraries worldwide
Representation Theory II Groups and Orders : Proceedings of the Fourth International Conference on Representations of Algebras
held in Ottawa, Canada, August 1625, 1984 by
Vlastimil Dlab(
)
2 editions published in 1986 in English and held by 68 WorldCat member libraries worldwide
2 editions published in 1986 in English and held by 68 WorldCat member libraries worldwide
Representation Theory I Finite Dimensional Algebras : Proceedings of the Fourth International Conference on Representations
of Algebras held in Ottawa, Canada, August 1625, 1984 by
Vlastimil Dlab(
)
2 editions published in 1986 in English and held by 68 WorldCat member libraries worldwide
2 editions published in 1986 in English and held by 68 WorldCat member libraries worldwide
Representation Theory I : Proceedings of the Workshop on the Present Trends in Representation Theory, Ottawa, Carleton University,
August 13  18, 1979 by
Vlastimil Dlab(
)
2 editions published in 1980 in English and held by 68 WorldCat member libraries worldwide
2 editions published in 1980 in English and held by 68 WorldCat member libraries worldwide
Representation Theory II Proceedings of the Second International Conference on Representations of Algebras Ottawa, Carleton
University, August 1325, 1979 by
Vlastimil Dlab(
)
1 edition published in 1980 in English and held by 32 WorldCat member libraries worldwide
1 edition published in 1980 in English and held by 32 WorldCat member libraries worldwide
Proceedings of the International Conference on Representations of Algebras by
Vlastimil Dlab(
Book
)
10 editions published between 1974 and 1975 in English and held by 27 WorldCat member libraries worldwide
10 editions published between 1974 and 1975 in English and held by 27 WorldCat member libraries worldwide
Des categories abeliennes by
Peter Gabriel(
Book
)
8 editions published between 1961 and 1962 in French and Undetermined and held by 22 WorldCat member libraries worldwide
8 editions published between 1961 and 1962 in French and Undetermined and held by 22 WorldCat member libraries worldwide
Schémas en groupes; séminaire de géométrie algébrique du Bois Marie, 1962/64, SGA 3 by
Michel Demazure(
Book
)
2 editions published in 2011 in French and held by 22 WorldCat member libraries worldwide
2 editions published in 2011 in French and held by 22 WorldCat member libraries worldwide
Representation theory III by Workshop on the Present Trends in Representation Theory(
Book
)
2 editions published in 1980 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1980 in English and held by 2 WorldCat member libraries worldwide
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Dlab, Vlastimil Other Author Editor
 Demazure, Michel Publishing director Author
 Michler, G. (Gerhard) 1938 Other Editor
 Zisman, Michel
 Borho, W. (Walter) 1945 Author
 Rentschler, Rudolf 1940
 Ulmer, Friedrich
 Serre, JeanPierre 1926 Author Collector
 Roĭter, A. V. (Andreĭ Vladimirovich) 1937
 SpringerLink (Service en ligne)
Useful Links
Associated Subjects
Abelian categories Abelian groups Algebra Algebraic fields Algebraic topology Algebras, Linear Associative algebras Categories (Mathematics) Dimension theory (Algebra) Finite groups Geometry Geometry, Algebraic Group algebras Group schemes (Mathematics) Group theory Homology theory Homotopy theory Ideals (Algebra) Lie algebras Linear algebraic groups Local rings Logic, Symbolic and mathematical Mathematics Matrices Modules (Algebra) Ordered groups Representations of algebras Representations of groups Rings (Algebra)
Alternative Names
Gabriel, P.
Gabriel, P. 1933
Gabriel, P. (Peter)
Gabriel, P. (Peter), 1933
Gabriel, Peter, 1933
Gabriel, Pierre.
Gabriel, Pierre 1933
Pierre Gabriel Frans wiskundige (19332015)
Pierre Gabriel fransk matematikar
Pierre Gabriel fransk matematiker
Pierre Gabriel französischer Mathematiker
Pierre Gabriel French mathematician
Pierre Gabriel matemático francés
Pierre Gabriel mathématicien français
Габриель, П..
Габриэль, Пьер
پییر گابریل ریاضیدان فرانسوی
ピエール・ガブリエル
Languages
Covers