The Relation Between Lie Groups and Lie Algebras
Identifieur interne : 001E63 ( Main/Exploration ); précédent : 001E62; suivant : 001E64The Relation Between Lie Groups and Lie Algebras
Auteurs : A. L. Onishchik [Russie]Source :
- Encyclopaedia of Mathematical Sciences [ 0938-0396 ] ; 1993.
Abstract
Abstract: The basic method of the theory of Lie groups, which makes it possible to obtain deep results with striking simplicity, consists in reducing questions concerning Lie groups to certain problems of linear algebra. This is done by assigning to every Lie group G its “tangent algebra”g, which to a large extent determines the group G, and to every homomorphism f: G → H of Lie groups a homomorphism df: g → h) of their tangent algebras, which to a large extent determines the homomorphism f. In the language of category theory we have a functor from the category of Lie groups into the category of Lie algebras, whose properties are very close to those of an equivalence of categories. In honour of the founder of the theory of Lie groups we will call this functor (following M. M. Postnikov (1982)) the Lie functor.
Url:
DOI: 10.1007/978-3-642-57999-8_3
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 001960
- to stream Istex, to step Curation: 001960
- to stream Istex, to step Checkpoint: 001C64
- to stream Main, to step Merge: 001E88
- to stream Main, to step Curation: 001E63
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">The Relation Between Lie Groups and Lie Algebras</title>
<author><name sortKey="Onishchik, A L" sort="Onishchik, A L" uniqKey="Onishchik A" first="A. L." last="Onishchik">A. L. Onishchik</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:7C41B9A7C4169522EDA25A1A3867525C8ECB0CA8</idno>
<date when="1993" year="1993">1993</date>
<idno type="doi">10.1007/978-3-642-57999-8_3</idno>
<idno type="url">https://api.istex.fr/document/7C41B9A7C4169522EDA25A1A3867525C8ECB0CA8/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">001960</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001960</idno>
<idno type="wicri:Area/Istex/Curation">001960</idno>
<idno type="wicri:Area/Istex/Checkpoint">001C64</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">001C64</idno>
<idno type="wicri:doubleKey">0938-0396:1993:Onishchik A:the:relation:between</idno>
<idno type="wicri:Area/Main/Merge">001E88</idno>
<idno type="wicri:Area/Main/Curation">001E63</idno>
<idno type="wicri:Area/Main/Exploration">001E63</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">The Relation Between Lie Groups and Lie Algebras</title>
<author><name sortKey="Onishchik, A L" sort="Onishchik, A L" uniqKey="Onishchik A" first="A. L." last="Onishchik">A. L. Onishchik</name>
<affiliation wicri:level="1"><country xml:lang="fr">Russie</country>
<wicri:regionArea>Yaroslavl University, Sovetskaya ul. 14, 150000, Yaroslavl</wicri:regionArea>
<wicri:noRegion>Yaroslavl</wicri:noRegion>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="s">Encyclopaedia of Mathematical Sciences</title>
<imprint><date>1993</date>
</imprint>
<idno type="ISSN">0938-0396</idno>
<idno type="ISSN">0938-0396</idno>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">0938-0396</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">Abstract: The basic method of the theory of Lie groups, which makes it possible to obtain deep results with striking simplicity, consists in reducing questions concerning Lie groups to certain problems of linear algebra. This is done by assigning to every Lie group G its “tangent algebra”g, which to a large extent determines the group G, and to every homomorphism f: G → H of Lie groups a homomorphism df: g → h) of their tangent algebras, which to a large extent determines the homomorphism f. In the language of category theory we have a functor from the category of Lie groups into the category of Lie algebras, whose properties are very close to those of an equivalence of categories. In honour of the founder of the theory of Lie groups we will call this functor (following M. M. Postnikov (1982)) the Lie functor.</div>
</front>
</TEI>
<affiliations><list><country><li>Russie</li>
</country>
</list>
<tree><country name="Russie"><noRegion><name sortKey="Onishchik, A L" sort="Onishchik, A L" uniqKey="Onishchik A" first="A. L." last="Onishchik">A. L. Onishchik</name>
</noRegion>
</country>
</tree>
</affiliations>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 001E63 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 001E63 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Mathematiques |area= BourbakiV1 |flux= Main |étape= Exploration |type= RBID |clé= ISTEX:7C41B9A7C4169522EDA25A1A3867525C8ECB0CA8 |texte= The Relation Between Lie Groups and Lie Algebras }}
This area was generated with Dilib version V0.6.33. |