skip to content
Theory of Lie groups. I Preview this item
ClosePreview this item
Checking...

Theory of Lie groups. I

Author: C Chevalley
Publisher: Princeton : Princeton University Press, 1946, [i.e. 1999]
Series: Princeton mathematical series, 8.; Princeton landmarks in mathematics and physics.
Edition/Format:   eBook : Document : English : Fifteenth printView all editions and formats
Database:WorldCat
Summary:
"This book was the first treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. To develop this idea to its fullest extent, Chevalley incorporated a broad range of topics, such as: the covering spaces of topological spaces, analytic manifolds, integration of complete systems of differential equations on a manifold, and  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Chevalley, C. (Claude), 1909-1984.
Theory of Lie groups. I.
Princeton : Princeton University Press, 1946, [i.e. 1999]
(OCoLC)44607709
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: C Chevalley
ISBN: 9781400883851 1400883857
OCLC Number: 948756345
Notes: Reprint. Originally published: Princeton, N.J. : Princeton University Press, 1946. (Princeton mathematical series ; 8) No more published in this edition?
Includes index.
Description: 1 online resource (viii, 217 pages)
Series Title: Princeton mathematical series, 8.; Princeton landmarks in mathematics and physics.
Responsibility: Claude Chevalley.

Abstract:

"This book was the first treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. To develop this idea to its fullest extent, Chevalley incorporated a broad range of topics, such as: the covering spaces of topological spaces, analytic manifolds, integration of complete systems of differential equations on a manifold, and the calculus of exterior differential forms." "The book opens with a short description of the classical groups: unitary groups, orthogonal groups, symplectic groups, etc. These special groups are then used to illustrate the general properties of Lie groups, which are considered later. The general notion of a Lie group is defined and correlated with the algebraic notion of a Lie algebra; the subgroups, factor groups, and homomorphisms of Lie groups are studied by making use of the Lie algebra. The last chapter is concerned with the theory of compact groups, culminating in Peter-Weyl's theorem on the existence of representations. Given a compact group, it is shown how one can construct algebraically the corresponding Lie group with complex parameters which appears in the form of a certain algebraic variety (associated algebraic group). This construction is intimately related to the proof of the generalization given by Tannaka of Pontrjagin's duality theorem for Abelian groups." "The continued importance of Lie groups in mathematics and theoretical physics makes this an indispensable volume for researchers in both fields."--Jacket.

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/948756345> # Theory of Lie groups. I
    a schema:CreativeWork, schema:MediaObject, schema:Book ;
    library:oclcnum "948756345" ;
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/nju> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/1815558426#Topic/mathematics_group_theory> ; # MATHEMATICS / Group Theory
    schema:about <http://experiment.worldcat.org/entity/work/data/1815558426#Topic/lie_groups> ; # Lie groups
    schema:about <http://dewey.info/class/512.55/e22/> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/1815558426#Topic/mathematics_algebra_intermediate> ; # MATHEMATICS / Algebra / Intermediate
    schema:bookEdition "Fifteenth print." ;
    schema:bookFormat schema:EBook ;
    schema:creator <http://experiment.worldcat.org/entity/work/data/1815558426#Person/chevalley_c_claude_1909_1984> ; # Claude Chevalley
    schema:datePublished "1999" ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/1815558426> ;
    schema:genre "Electronic books"@en ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/1815558426#Series/princeton_landmarks_in_mathematics_and_physics> ; # Princeton landmarks in mathematics and physics.
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/1815558426#Series/princeton_mathematical_series> ; # Princeton mathematical series ;
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/1815558426#Series/princeton_landmarks_in_mathematics> ; # Princeton landmarks in mathematics
    schema:isSimilarTo <http://www.worldcat.org/oclc/44607709> ;
    schema:name "Theory of Lie groups. I"@en ;
    schema:productID "948756345" ;
    schema:reviews <http://www.worldcat.org/title/-/oclc/948756345#Review/-2017916200> ;
    schema:url <http://www.jstor.org/stable/10.2307/j.ctt1bpm9z7> ;
    schema:url <http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=1231064> ;
    schema:workExample <http://worldcat.org/isbn/9781400883851> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/948756345> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/1815558426#Person/chevalley_c_claude_1909_1984> # Claude Chevalley
    a schema:Person ;
    schema:birthDate "1909" ;
    schema:deathDate "1984" ;
    schema:familyName "Chevalley" ;
    schema:givenName "Claude" ;
    schema:givenName "C." ;
    schema:name "Claude Chevalley" ;
    .

<http://experiment.worldcat.org/entity/work/data/1815558426#Series/princeton_landmarks_in_mathematics> # Princeton landmarks in mathematics
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/948756345> ; # Theory of Lie groups. I
    schema:name "Princeton landmarks in mathematics" ;
    .

<http://experiment.worldcat.org/entity/work/data/1815558426#Series/princeton_landmarks_in_mathematics_and_physics> # Princeton landmarks in mathematics and physics.
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/948756345> ; # Theory of Lie groups. I
    schema:name "Princeton landmarks in mathematics and physics." ;
    .

<http://experiment.worldcat.org/entity/work/data/1815558426#Series/princeton_mathematical_series> # Princeton mathematical series ;
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/948756345> ; # Theory of Lie groups. I
    schema:name "Princeton mathematical series ;" ;
    .

<http://experiment.worldcat.org/entity/work/data/1815558426#Topic/mathematics_algebra_intermediate> # MATHEMATICS / Algebra / Intermediate
    a schema:Intangible ;
    schema:name "MATHEMATICS / Algebra / Intermediate"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/1815558426#Topic/mathematics_group_theory> # MATHEMATICS / Group Theory
    a schema:Intangible ;
    schema:name "MATHEMATICS / Group Theory"@en ;
    .

<http://worldcat.org/isbn/9781400883851>
    a schema:ProductModel ;
    schema:isbn "1400883857" ;
    schema:isbn "9781400883851" ;
    .

<http://www.worldcat.org/oclc/44607709>
    a schema:CreativeWork ;
    rdfs:label "Theory of Lie groups. I." ;
    schema:description "Print version:" ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/948756345> ; # Theory of Lie groups. I
    .

<http://www.worldcat.org/title/-/oclc/948756345#Review/-2017916200>
    a schema:Review ;
    schema:itemReviewed <http://www.worldcat.org/oclc/948756345> ; # Theory of Lie groups. I
    schema:reviewBody ""This book was the first treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. To develop this idea to its fullest extent, Chevalley incorporated a broad range of topics, such as: the covering spaces of topological spaces, analytic manifolds, integration of complete systems of differential equations on a manifold, and the calculus of exterior differential forms." "The book opens with a short description of the classical groups: unitary groups, orthogonal groups, symplectic groups, etc. These special groups are then used to illustrate the general properties of Lie groups, which are considered later. The general notion of a Lie group is defined and correlated with the algebraic notion of a Lie algebra; the subgroups, factor groups, and homomorphisms of Lie groups are studied by making use of the Lie algebra. The last chapter is concerned with the theory of compact groups, culminating in Peter-Weyl's theorem on the existence of representations. Given a compact group, it is shown how one can construct algebraically the corresponding Lie group with complex parameters which appears in the form of a certain algebraic variety (associated algebraic group). This construction is intimately related to the proof of the generalization given by Tannaka of Pontrjagin's duality theorem for Abelian groups." "The continued importance of Lie groups in mathematics and theoretical physics makes this an indispensable volume for researchers in both fields."--Jacket." ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.