Hochschild, Gerhard P. (Gerhard Paul) 1915
Overview
Works:  23 works in 136 publications in 4 languages and 2,293 library holdings 

Roles:  Author, Contributor, Editor 
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Most widely held works about
Gerhard P Hochschild
 Hochschild Festschrift( Book )
 Gerhard P. Hochschild papers by Gerhard P Hochschild( )
Most widely held works by
Gerhard P Hochschild
The structure of Lie groups by
Gerhard P Hochschild(
Book
)
36 editions published between 1965 and 1969 in English and French and held by 675 WorldCat member libraries worldwide
36 editions published between 1965 and 1969 in English and French and held by 675 WorldCat member libraries worldwide
Basic theory of algebraic groups and Lie algebras by
Gerhard P Hochschild(
Book
)
17 editions published in 1981 in English and German and held by 527 WorldCat member libraries worldwide
The theory of algebraic groups results from the interaction of various basic techniques from field theory, multilinear algebra, commutative ring theory, algebraic geometry and general algebraic representation theory of groups and Lie algebras. It is thus an ideally suitable framework for exhibiting basic algebra in action. To do that is the principal concern of this text. Accordingly, its emphasis is on developing the major general mathematical tools used for gaining control over algebraic groups, rather than on securing the final definitive results, such as the classification of the simple groups and their irreducible representations. In the same spirit, this exposition has been made entirely selfcontained; no detailed knowledge beyond the usual standard material of the first one or two years of graduate study in algebra is pre supposed. The chapter headings should be sufficient indication of the content and organisation of this book. Each chapter begins with a brief announcement of its results and ends with a few notes ranging from supplementary results, amplifications of proofs, examples and counterexamples through exercises to references. The references are intended to be merely suggestions for supplementary reading or indications of original sources, especially in cases where these might not be the expected ones. Algebraic group theory has reached a state of maturity and perfection where it may no longer be necessary to reiterate an account of its genesis. Of the material to be presented here, including much of the basic support, the major portion is due to Claude Chevalley
17 editions published in 1981 in English and German and held by 527 WorldCat member libraries worldwide
The theory of algebraic groups results from the interaction of various basic techniques from field theory, multilinear algebra, commutative ring theory, algebraic geometry and general algebraic representation theory of groups and Lie algebras. It is thus an ideally suitable framework for exhibiting basic algebra in action. To do that is the principal concern of this text. Accordingly, its emphasis is on developing the major general mathematical tools used for gaining control over algebraic groups, rather than on securing the final definitive results, such as the classification of the simple groups and their irreducible representations. In the same spirit, this exposition has been made entirely selfcontained; no detailed knowledge beyond the usual standard material of the first one or two years of graduate study in algebra is pre supposed. The chapter headings should be sufficient indication of the content and organisation of this book. Each chapter begins with a brief announcement of its results and ends with a few notes ranging from supplementary results, amplifications of proofs, examples and counterexamples through exercises to references. The references are intended to be merely suggestions for supplementary reading or indications of original sources, especially in cases where these might not be the expected ones. Algebraic group theory has reached a state of maturity and perfection where it may no longer be necessary to reiterate an account of its genesis. Of the material to be presented here, including much of the basic support, the major portion is due to Claude Chevalley
Introduction to affine algebraic groups by
Gerhard P Hochschild(
Book
)
10 editions published in 1971 in English and held by 340 WorldCat member libraries worldwide
10 editions published in 1971 in English and held by 340 WorldCat member libraries worldwide
Perspectives of elementary mathematics by
Gerhard P Hochschild(
Book
)
16 editions published in 1983 in English and German and held by 300 WorldCat member libraries worldwide
Primarily, this book addresses beginning graduate students expecting to become mathematicians or mathematically oriented computer scientists. Accordingly, the presentation is conditioned in content as well as in form by the assumption that the reader has already made an internal commitment to mathematics and is seeking not only mathematical information but also active involvement with mathematical pursuits. The general aim of what follows is to present basic mathematical concepts and techniques in familiar contexts in such a way as to illuminate the nature of mathematics as an art. Thus, the selection and organization of the material is based on considerations regarding the philosophical significance of various mathematical notions and results, their interdependence and their accessi bility. In other words, this text concentrates on displaying coherent mathe matical material meriting exceptionally careful and expansive contemplation. It should not be regarded as a reference for the most frequently used results or methods of elementary mathematics. The exposition is meant to be reasonably selfcontained and to embody a growth pattern of mathematical ideas (for which no historical validity is claimed, of course). In order to avoid burying the essentials under routine technicalities, a style has been adopted that relies on the reader's active involvement somewhat more than is customary in texts for beginners. The exercises proposed at the end of each chapter are frequently extensions of the chapter content, rather than mere illustrations. They are designed to be manageable in a straightforward fashion within the framework provided by the text
16 editions published in 1983 in English and German and held by 300 WorldCat member libraries worldwide
Primarily, this book addresses beginning graduate students expecting to become mathematicians or mathematically oriented computer scientists. Accordingly, the presentation is conditioned in content as well as in form by the assumption that the reader has already made an internal commitment to mathematics and is seeking not only mathematical information but also active involvement with mathematical pursuits. The general aim of what follows is to present basic mathematical concepts and techniques in familiar contexts in such a way as to illuminate the nature of mathematics as an art. Thus, the selection and organization of the material is based on considerations regarding the philosophical significance of various mathematical notions and results, their interdependence and their accessi bility. In other words, this text concentrates on displaying coherent mathe matical material meriting exceptionally careful and expansive contemplation. It should not be regarded as a reference for the most frequently used results or methods of elementary mathematics. The exposition is meant to be reasonably selfcontained and to embody a growth pattern of mathematical ideas (for which no historical validity is claimed, of course). In order to avoid burying the essentials under routine technicalities, a style has been adopted that relies on the reader's active involvement somewhat more than is customary in texts for beginners. The exercises proposed at the end of each chapter are frequently extensions of the chapter content, rather than mere illustrations. They are designed to be manageable in a straightforward fashion within the framework provided by the text
A second introduction to analytic geometry by
Gerhard P Hochschild(
Book
)
8 editions published in 1968 in English and held by 194 WorldCat member libraries worldwide
8 editions published in 1968 in English and held by 194 WorldCat member libraries worldwide
Representation theory of Lie algebras by
Gerhard P Hochschild(
Book
)
16 editions published in 1959 in English and held by 188 WorldCat member libraries worldwide
16 editions published in 1959 in English and held by 188 WorldCat member libraries worldwide
Phasensynchronisierung supraleitender Beschleunigungsresonatoren by
Gerhard P Hochschild(
Book
)
6 editions published between 1974 and 1975 in German and Undetermined and held by 22 WorldCat member libraries worldwide
6 editions published between 1974 and 1975 in German and Undetermined and held by 22 WorldCat member libraries worldwide
Representation theory of Lie algebras; notes by G. Leger by
Gerhard P Hochschild(
Book
)
3 editions published in 1959 in English and held by 9 WorldCat member libraries worldwide
3 editions published in 1959 in English and held by 9 WorldCat member libraries worldwide
A linear postaccelerator with superconducting helix resonators for medium mass ions preparatory experiments and conceptual
design(
Book
)
4 editions published in 1978 in English and German and held by 8 WorldCat member libraries worldwide
4 editions published in 1978 in English and German and held by 8 WorldCat member libraries worldwide
Ein supraleitender WendelNachbeschleuniger für mittelschwere Ionen experimentelle Vorarbeiten u. Entwurf by
Gerhard P Hochschild(
Book
)
2 editions published in 1977 in German and held by 7 WorldCat member libraries worldwide
2 editions published in 1977 in German and held by 7 WorldCat member libraries worldwide
Semisimple algebras and generalized derivations by
Gerhard P Hochschild(
Book
)
2 editions published between 1941 and 1942 in English and held by 5 WorldCat member libraries worldwide
2 editions published between 1941 and 1942 in English and held by 5 WorldCat member libraries worldwide
Rīgun no kōzō(
Book
)
3 editions published in 1972 in Japanese and held by 3 WorldCat member libraries worldwide
3 editions published in 1972 in Japanese and held by 3 WorldCat member libraries worldwide
Differential forms on regular affine algebra by
Gerhard P Hochschild(
Book
)
2 editions published in 1961 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1961 in English and held by 2 WorldCat member libraries worldwide
Extensions of representations of Lie groups and Lie algebras. I. by
Gerhard P Hochschild(
Book
)
1 edition published in 1957 in English and held by 1 WorldCat member library worldwide
1 edition published in 1957 in English and held by 1 WorldCat member library worldwide
Differential forms and lie algebra cohomology for algebraic linear groups(
Book
)
1 edition published in 1961 in English and held by 1 WorldCat member library worldwide
1 edition published in 1961 in English and held by 1 WorldCat member library worldwide
Differential forms on regular affine algebra(
Book
)
1 edition published in 1961 in English and held by 1 WorldCat member library worldwide
A mathematical discussion of the algebras of differential forms is treated as a special combination of linear algebra and homological alegbra. There is specific identification of this particular exterior algebra as applied to canical graded algebra based on the Tor functor and obtained by the cohomology of differential forms from the ext functor to a universal algebra i. e. Lie algebra. Attention is directed chiefly to a regular affine algebra, Kalgebra, which is Noetherian with a finite Krull dimension, i. e. the largest nonnegative integer
1 edition published in 1961 in English and held by 1 WorldCat member library worldwide
A mathematical discussion of the algebras of differential forms is treated as a special combination of linear algebra and homological alegbra. There is specific identification of this particular exterior algebra as applied to canical graded algebra based on the Tor functor and obtained by the cohomology of differential forms from the ext functor to a universal algebra i. e. Lie algebra. Attention is directed chiefly to a regular affine algebra, Kalgebra, which is Noetherian with a finite Krull dimension, i. e. the largest nonnegative integer
ECRH and gyrotrons : joint USSRFRG meeting, March 6  10, 1989, Stuttgart, Karlsruhe; workshop contributions(
Book
)
1 edition published in 1989 in Undetermined and held by 1 WorldCat member library worldwide
1 edition published in 1989 in Undetermined and held by 1 WorldCat member library worldwide
[Algebraic number theory] by
Gerhard P Hochschild(
Book
)
in English and held by 1 WorldCat member library worldwide
in English and held by 1 WorldCat member library worldwide
La sructure des groupes de lie by
Gerhard P Hochschild(
Book
)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
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Affine algebraic groups Algebra, Abstract Algebra, Universal Algebraic number theory CaliforniaBerkeley Continuous groups Dedekind rings Differential forms Geometry, Analytic Group theory Hochschild, Gerhard P.(Gerhard Paul), Hopf algebras Lie algebras Lie groups Linear algebraic groups Logic, Symbolic and mathematical Mathematicians Mathematics Representations of algebras Representations of groups Topological groups Universities and collegesFaculty University of California, Berkeley.Department of Mathematics
Alternative Names
Gerhard Hochschild Amerikaans wiskundige (19152010)
Gerhard Hochschild amerikansk matematikar
Gerhard Hochschild amerikansk matematiker
Gerhard Hochschild matemàtic estatunidenc
Gerhard Hochschild matemático estadounidense
Gerhard Hochschild matematico statunitense
Gerhard Hochschild mathématicien américain
Gerhard Hochschild USamerikanischer Mathematiker
Hochschild, G.
Hochschild, G. 1915
Hochschild, G. 19152010
Hochschild, G. (Gerhard)
Hochschild, G. (Gerhard), 1915
Hochschild, G. P. 19152010
Hochschild, Gerhard 19152010
Hochschild, Gerhard P.
Hochschild, Gerhard P. 1915
Hochschild, Gerhard P. (Gerhard Paul), 1915
Hochschild, Gerhard Paul
Hochschild, Gerhard Paul 1915
Hochschild, Gerhard Paul 19152010
Герхард Хохшилд
Герхард Хохшильд германоамериканский математик
게르하르트 호흐실트
ゲルハルト・ホッホシルト
ホッホシルト
格哈德·霍赫希尔德
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