Ontology type: schema:ScholarlyArticle
2019-03-20
AUTHORSAlfons I. Ooms
ABSTRACTA finite dimensional Lie algebra L with magic number c(L) is said to satisfy Rentschler’s property if it admits an abelian Lie subalgebra H of dimension at least c(L) − 1. We study the occurrence of this new property in various Lie algebras, such as nonsolvable, solvable, nilpotent, metabelian and filiform Lie algebras. Under some mild condition H gives rise to a complete Poisson commutative subalgebra of the symmetric algebra S(L). Using this, we show that Milovanov’s conjecture holds for the filiform Lie algebras of type Ln, Qn, Rn, Wn and also for all filiform Lie algebras of dimension at most eight. For the latter the Poisson center of these Lie algebras is determined. More... »
PAGES1-37
http://scigraph.springernature.com/pub.10.1007/s10468-019-09877-5
DOIhttp://dx.doi.org/10.1007/s10468-019-09877-5
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1112896825
JSON-LD is the canonical representation for SciGraph data.
TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT
[
{
"@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json",
"about": [
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Pure Mathematics",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Mathematical Sciences",
"type": "DefinedTerm"
}
],
"author": [
{
"affiliation": {
"alternateName": "University of Hasselt",
"id": "https://www.grid.ac/institutes/grid.12155.32",
"name": [
"Mathematics Department, Hasselt University, Agoralaan, Campus Diepenbeek, 3590, Diepenbeek, Belgium"
],
"type": "Organization"
},
"familyName": "Ooms",
"givenName": "Alfons I.",
"type": "Person"
}
],
"citation": [
{
"id": "https://doi.org/10.1016/j.jalgebra.2006.12.026",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1003678694"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1090/s0002-9939-1957-0083101-4",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1004734881"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1080/00927870601141936",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1004743428"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1112/jlms/s2-3.4.731",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1004809074"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1090/s0002-9904-1944-08169-x",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1005035445"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01076005",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1007435015",
"https://doi.org/10.1007/bf01076005"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10587-013-0057-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1008250442",
"https://doi.org/10.1007/s10587-013-0057-6"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/s0021-8693(03)00146-7",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1008266899"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/s0021-8693(03)00146-7",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1008266899"
],
"type": "CreativeWork"
},
{
"id": "https://app.dimensions.ai/details/publication/pub.1009689331",
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-94-017-2432-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1009689331",
"https://doi.org/10.1007/978-94-017-2432-6"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-94-017-2432-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1009689331",
"https://doi.org/10.1007/978-94-017-2432-6"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.jalgebra.2012.04.029",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1010466720"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10468-010-9260-4",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1015515107",
"https://doi.org/10.1007/s10468-010-9260-4"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10468-010-9260-4",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1015515107",
"https://doi.org/10.1007/s10468-010-9260-4"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1515/crll.1905.130.66",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1015898131"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1080/00927878008822445",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1017470342"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/s0022-4049(97)00096-0",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1019925214"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s11232-007-0107-z",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1021081841",
"https://doi.org/10.1007/s11232-007-0107-z"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1006/jabr.1999.8192",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1024235905"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1080/00207160.2012.688112",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1025781847"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.3103/s0027132211050044",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1026021332",
"https://doi.org/10.3103/s0027132211050044"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.jalgebra.2008.10.026",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1029992640"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00031-010-9113-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1030586734",
"https://doi.org/10.1007/s00031-010-9113-6"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00031-010-9113-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1030586734",
"https://doi.org/10.1007/s00031-010-9113-6"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00222-003-0337-0",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1035831617",
"https://doi.org/10.1007/s00222-003-0337-0"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.jalgebra.2009.09.017",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1036529529"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0021-8693(76)90114-9",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1037943486"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01193621",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1038149935",
"https://doi.org/10.1007/bf01193621"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01193621",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1038149935",
"https://doi.org/10.1007/bf01193621"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.jpaa.2013.06.017",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1040560151"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1006/jabr.2000.8342",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1041795213"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.jalgebra.2003.11.004",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1041975509"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00607-009-0029-8",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1043307806",
"https://doi.org/10.1007/s00607-009-0029-8"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00607-009-0029-8",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1043307806",
"https://doi.org/10.1007/s00607-009-0029-8"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00607-009-0029-8",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1043307806",
"https://doi.org/10.1007/s00607-009-0029-8"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.jalgebra.2016.12.009",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1044728329"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1090/s0002-9939-1993-1139475-8",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1045374832"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10958-008-0052-x",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1050108347",
"https://doi.org/10.1007/s10958-008-0052-x"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1515/form.2003.024",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1053285692"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1070/sm2009v200n12abeh004057",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1058202520"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1070/sm2009v200n12abeh004057",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1058202520"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.4310/mrl.2008.v15.n2.a3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1072462608"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.7153/mia-13-43",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1073624869"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.7153/mia-13-43",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1073624869"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.7153/mia-13-43",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1073624869"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.7153/mia-13-43",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1073624869"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.7153/mia-13-43",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1073624869"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.24033/bsmf.1695",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1083660659"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1080/00029890.1998.12004879",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1103599980"
],
"type": "CreativeWork"
}
],
"datePublished": "2019-03-20",
"datePublishedReg": "2019-03-20",
"description": "A finite dimensional Lie algebra L with magic number c(L) is said to satisfy Rentschler\u2019s property if it admits an abelian Lie subalgebra H of dimension at least c(L) \u2212 1. We study the occurrence of this new property in various Lie algebras, such as nonsolvable, solvable, nilpotent, metabelian and filiform Lie algebras. Under some mild condition H gives rise to a complete Poisson commutative subalgebra of the symmetric algebra S(L). Using this, we show that Milovanov\u2019s conjecture holds for the filiform Lie algebras of type Ln, Qn, Rn, Wn and also for all filiform Lie algebras of dimension at most eight. For the latter the Poisson center of these Lie algebras is determined.",
"genre": "research_article",
"id": "sg:pub.10.1007/s10468-019-09877-5",
"inLanguage": [
"en"
],
"isAccessibleForFree": false,
"isPartOf": [
{
"id": "sg:journal.1136385",
"issn": [
"1386-923X",
"1572-9079"
],
"name": "Algebras and Representation Theory",
"type": "Periodical"
}
],
"name": "The Maximal Abelian Dimension of a Lie Algebra, Rentschler\u2019s Property and Milovanov\u2019s Conjecture",
"pagination": "1-37",
"productId": [
{
"name": "readcube_id",
"type": "PropertyValue",
"value": [
"3504af789f0d1f384faec3a694ddd97f43af420f3d0fad356728ae5818daeb85"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/s10468-019-09877-5"
]
},
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1112896825"
]
}
],
"sameAs": [
"https://doi.org/10.1007/s10468-019-09877-5",
"https://app.dimensions.ai/details/publication/pub.1112896825"
],
"sdDataset": "articles",
"sdDatePublished": "2019-04-11T12:40",
"sdLicense": "https://scigraph.springernature.com/explorer/license/",
"sdPublisher": {
"name": "Springer Nature - SN SciGraph project",
"type": "Organization"
},
"sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000363_0000000363/records_70046_00000003.jsonl",
"type": "ScholarlyArticle",
"url": "https://link.springer.com/10.1007%2Fs10468-019-09877-5"
}
]Download the RDF metadata as: json-ld nt turtle xml License info
JSON-LD is a popular format for linked data which is fully compatible with JSON.
curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s10468-019-09877-5'
N-Triples is a line-based linked data format ideal for batch operations.
curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s10468-019-09877-5'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10468-019-09877-5'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10468-019-09877-5'
This table displays all metadata directly associated to this object as RDF triples.
178 TRIPLES
21 PREDICATES
62 URIs
16 LITERALS
5 BLANK NODES