Zariski density in lie groups
Identifieur interne : 003173 ( Istex/Corpus ); précédent : 003172; suivant : 003174Zariski density in lie groups
Auteurs : Richard D. Mosak ; Martin MoskowitzSource :
- Israel Journal of Mathematics [ 0021-2172 ] ; 1985-03-01.
English descriptors
- KwdEn :
- Abelian, Abelian subgroup, Acts semisimply, Borel density theorem, Chabauty, Chabauty topology, Compact group, Density theorem, Eigenvalue, Finite index, Finite volume, Moskowitz, Other hand, Quasibounded, Quasibounded groups, Real eigenvalues, Semisimple, Solvable, Subgroup, Topology, Triangularizable, Vector group, Zariski, Zariski density.
- Teeft :
- Abelian, Abelian subgroup, Acts semisimply, Borel density theorem, Chabauty, Chabauty topology, Compact group, Density theorem, Eigenvalue, Finite index, Finite volume, Moskowitz, Other hand, Quasibounded, Quasibounded groups, Real eigenvalues, Semisimple, Solvable, Subgroup, Topology, Triangularizable, Vector group, Zariski, Zariski density.
Abstract
Abstract: In [7] Furstenberg gave a proof of Borel’s density theorem [1], which depended not on complete reducibility but rather on properties of the action of a minimally almost periodic group on projective space. In [9] and [10] the basic idea of this proof was extended in various ways to deal with other particular classes of Lie groupsG and closed subgroupsH of cofinite volume. In [5] Dani gives a more general form of the density theorem in whichH need only be non-wandering. In the present paper we define the condition ofk-minimal quasiboundedness, and prove that this condition is necessary and sufficient for the density theorem to hold ((2.4) and (2.6)). Here we replace the arguments of [9] and [10] simply by proofs that the groups considered there satisfy this condition (2.10). We extend the results of [9] and [10] by considering groups which are analytic rather than algebraic, and in the solvable case we completely characterize thek-minimally quasibounded groups (2.9). In the last section we give two applications of the density theorem.
Url:
DOI: 10.1007/BF02776074
Links to Exploration step
ISTEX:F2D4F77D74FAAC4EE62303539CD14FC66A6E4E6DLe document en format XML
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In [9] and [10] the basic idea of this proof was extended in various ways to deal with other particular classes of Lie groups<Emphasis Type="Italic">G</Emphasis> and closed subgroups<Emphasis Type="Italic">H</Emphasis> of cofinite volume. In [5] Dani gives a more general form of the density theorem in which<Emphasis Type="Italic">H</Emphasis> need only be non-wandering. In the present paper we define the condition of<Emphasis Type="Italic">k</Emphasis>-minimal quasiboundedness, and prove that this condition is necessary and sufficient for the density theorem to hold ((2.4) and (2.6)). Here we replace the arguments of [9] and [10] simply by proofs that the groups considered there satisfy this condition (2.10). We extend the results of [9] and [10] by considering groups which are analytic rather than algebraic, and in the solvable case we completely characterize the<Emphasis Type="Italic">k</Emphasis>-minimally quasibounded groups (2.9). In the last section we give two applications of the density theorem.</Para></Abstract></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Zariski density in lie groups</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Zariski density in lie groups</title></titleInfo><name type="personal"><namePart type="given">Richard</namePart><namePart type="given">D.</namePart><namePart type="family">Mosak</namePart><affiliation>Department of Mathematics and Computer Science, Lehman College, CUNY, 10468, Bronx, NY, USA</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Martin</namePart><namePart type="family">Moskowitz</namePart><affiliation>Department of Mathematics, Graduate Center, CUNY, 10036, New York, NY, USA</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Springer-Verlag</publisher><place><placeTerm type="text">New York</placeTerm></place><dateCreated encoding="w3cdtf">1984-03-13</dateCreated><dateIssued encoding="w3cdtf">1985-03-01</dateIssued><dateIssued encoding="w3cdtf">1985</dateIssued><copyrightDate encoding="w3cdtf">1985</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: In [7] Furstenberg gave a proof of Borel’s density theorem [1], which depended not on complete reducibility but rather on properties of the action of a minimally almost periodic group on projective space. In [9] and [10] the basic idea of this proof was extended in various ways to deal with other particular classes of Lie groupsG and closed subgroupsH of cofinite volume. In [5] Dani gives a more general form of the density theorem in whichH need only be non-wandering. In the present paper we define the condition ofk-minimal quasiboundedness, and prove that this condition is necessary and sufficient for the density theorem to hold ((2.4) and (2.6)). Here we replace the arguments of [9] and [10] simply by proofs that the groups considered there satisfy this condition (2.10). We extend the results of [9] and [10] by considering groups which are analytic rather than algebraic, and in the solvable case we completely characterize thek-minimally quasibounded groups (2.9). In the last section we give two applications of the density theorem.</abstract><relatedItem type="host"><titleInfo><title>Israel Journal of Mathematics</title></titleInfo><titleInfo type="abbreviated"><title>Israel J. Math.</title></titleInfo><genre type="journal" displayLabel="Archive Journal" authority="ISTEX" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre><originInfo><publisher>Springer</publisher><dateIssued encoding="w3cdtf">1985-03-01</dateIssued><copyrightDate encoding="w3cdtf">1985</copyrightDate></originInfo><subject><genre>Journal-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="M">Mathematics</topic><topic authority="SpringerSubjectCodes" authorityURI="M00009">Mathematics, general</topic><topic authority="SpringerSubjectCodes" authorityURI="M11000">Algebra</topic><topic authority="SpringerSubjectCodes" authorityURI="M11078">Group Theory and Generalizations</topic><topic authority="SpringerSubjectCodes" authorityURI="M12007">Analysis</topic><topic authority="SpringerSubjectCodes" authorityURI="M13003">Applications of Mathematics</topic><topic authority="SpringerSubjectCodes" authorityURI="P19005">Mathematical and Computational Physics</topic></subject><identifier type="ISSN">0021-2172</identifier><identifier type="eISSN">1565-8511</identifier><identifier type="JournalID">11856</identifier><identifier type="IssueArticleCount">16</identifier><identifier type="VolumeIssueCount">4</identifier><part><date>1985</date><detail type="volume"><number>52</number><caption>vol.</caption></detail><detail type="issue"><number>1-2</number><caption>no.</caption></detail><extent unit="pages"><start>1</start><end>14</end></extent></part><recordInfo><recordOrigin>Hebrew University, 1985</recordOrigin></recordInfo></relatedItem><identifier type="istex">F2D4F77D74FAAC4EE62303539CD14FC66A6E4E6D</identifier><identifier type="ark">ark:/67375/1BB-C8935TMV-L</identifier><identifier type="DOI">10.1007/BF02776074</identifier><identifier type="ArticleID">BF02776074</identifier><identifier type="ArticleID">Art1</identifier><accessCondition type="use and reproduction" contentType="copyright">The Weizmann Science Press of Israel, 1985</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-3XSW68JL-F">springer</recordContentSource><recordOrigin>The Weizmann Science Press of Israel, 1985</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/document/F2D4F77D74FAAC4EE62303539CD14FC66A6E4E6D/metadata/json</uri></json:item></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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