Solvable Lie algebras with naturally graded nilradicals and their invariants

Solvable Lie algebras with naturally graded nilradicals and their invariants

The indecomposable solvable Lie algebras with graded nilradical of maximal nilindex and a Heisenberg subalgebra of codimension one are analyzed, and their generalized Casimir invariants calculated. It is shown that rank one solvable algebras have a contact form, which implies the existence of an ass...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2006-02
Hauptverfasser: Ancochea, J M, Campoamor-Stursberg, R, L Garcia Vergnolle
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Ghosts
Invariants
Lie groups
Quantum theory
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Ancochea, J M
Campoamor-Stursberg, R
L Garcia Vergnolle
description The indecomposable solvable Lie algebras with graded nilradical of maximal nilindex and a Heisenberg subalgebra of codimension one are analyzed, and their generalized Casimir invariants calculated. It is shown that rank one solvable algebras have a contact form, which implies the existence of an associated dynamical system. Moreover, due to the structure of the quadratic Casimir operator of the nilradical, these algebras contain a maximal non-abelian quasi-classical Lie algebra of dimension \(2n-1\), indicating that gauge theories (with ghosts) are possible on these subalgebras.
doi_str_mv 10.48550/arxiv.0511027
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2090040035</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2090040035</sourcerecordid><originalsourceid>FETCH-proquest_journals_20900400353</originalsourceid><addsrcrecordid>eNqNij0LwjAUAIMgKOrq_MDZ-po0fsyiOHTTvbzaqJGQ6kta9d_bwR_gdAd3QkxTTLK11rggfts2QZ2mKFc9MZRKpfN1JuVATEK4I6JcrqTWaijyY-1aKp2B3BogdzUlU4CXjTfwFBsm5z5wZapMBd66TuyZXADyFcSbsQzWt8SWfAxj0b90zUx-HInZfnfaHuYPrp-NCbG41w37LhUSN4gZotLqv-sLDNpDVw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2090040035</pqid></control><display><type>article</type><title>Solvable Lie algebras with naturally graded nilradicals and their invariants</title><source>Free E- Journals</source><creator>Ancochea, J M ; Campoamor-Stursberg, R ; L Garcia Vergnolle</creator><creatorcontrib>Ancochea, J M ; Campoamor-Stursberg, R ; L Garcia Vergnolle</creatorcontrib><description>The indecomposable solvable Lie algebras with graded nilradical of maximal nilindex and a Heisenberg subalgebra of codimension one are analyzed, and their generalized Casimir invariants calculated. It is shown that rank one solvable algebras have a contact form, which implies the existence of an associated dynamical system. Moreover, due to the structure of the quadratic Casimir operator of the nilradical, these algebras contain a maximal non-abelian quasi-classical Lie algebra of dimension \(2n-1\), indicating that gauge theories (with ghosts) are possible on these subalgebras.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.0511027</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Algebra ; Ghosts ; Invariants ; Lie groups ; Quantum theory</subject><ispartof>arXiv.org, 2006-02</ispartof><rights>Notwithstanding the ProQuest Terms and conditions, you may use this content in accordance with the associated terms available at http://arxiv.org/abs/math-ph/0511027.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>780,784,27923</link.rule.ids></links><search><creatorcontrib>Ancochea, J M</creatorcontrib><creatorcontrib>Campoamor-Stursberg, R</creatorcontrib><creatorcontrib>L Garcia Vergnolle</creatorcontrib><title>Solvable Lie algebras with naturally graded nilradicals and their invariants</title><title>arXiv.org</title><description>The indecomposable solvable Lie algebras with graded nilradical of maximal nilindex and a Heisenberg subalgebra of codimension one are analyzed, and their generalized Casimir invariants calculated. It is shown that rank one solvable algebras have a contact form, which implies the existence of an associated dynamical system. Moreover, due to the structure of the quadratic Casimir operator of the nilradical, these algebras contain a maximal non-abelian quasi-classical Lie algebra of dimension \(2n-1\), indicating that gauge theories (with ghosts) are possible on these subalgebras.</description><subject>Algebra</subject><subject>Ghosts</subject><subject>Invariants</subject><subject>Lie groups</subject><subject>Quantum theory</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNij0LwjAUAIMgKOrq_MDZ-po0fsyiOHTTvbzaqJGQ6kta9d_bwR_gdAd3QkxTTLK11rggfts2QZ2mKFc9MZRKpfN1JuVATEK4I6JcrqTWaijyY-1aKp2B3BogdzUlU4CXjTfwFBsm5z5wZapMBd66TuyZXADyFcSbsQzWt8SWfAxj0b90zUx-HInZfnfaHuYPrp-NCbG41w37LhUSN4gZotLqv-sLDNpDVw</recordid><startdate>20060201</startdate><enddate>20060201</enddate><creator>Ancochea, J M</creator><creator>Campoamor-Stursberg, R</creator><creator>L Garcia Vergnolle</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20060201</creationdate><title>Solvable Lie algebras with naturally graded nilradicals and their invariants</title><author>Ancochea, J M ; Campoamor-Stursberg, R ; L Garcia Vergnolle</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20900400353</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Algebra</topic><topic>Ghosts</topic><topic>Invariants</topic><topic>Lie groups</topic><topic>Quantum theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Ancochea, J M</creatorcontrib><creatorcontrib>Campoamor-Stursberg, R</creatorcontrib><creatorcontrib>L Garcia Vergnolle</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ancochea, J M</au><au>Campoamor-Stursberg, R</au><au>L Garcia Vergnolle</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Solvable Lie algebras with naturally graded nilradicals and their invariants</atitle><jtitle>arXiv.org</jtitle><date>2006-02-01</date><risdate>2006</risdate><eissn>2331-8422</eissn><abstract>The indecomposable solvable Lie algebras with graded nilradical of maximal nilindex and a Heisenberg subalgebra of codimension one are analyzed, and their generalized Casimir invariants calculated. It is shown that rank one solvable algebras have a contact form, which implies the existence of an associated dynamical system. Moreover, due to the structure of the quadratic Casimir operator of the nilradical, these algebras contain a maximal non-abelian quasi-classical Lie algebra of dimension \(2n-1\), indicating that gauge theories (with ghosts) are possible on these subalgebras.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.0511027</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2006-02
issn 2331-8422
language eng
recordid cdi_proquest_journals_2090040035
source Free E- Journals
subjects Algebra
Ghosts
Invariants
Lie groups
Quantum theory
title Solvable Lie algebras with naturally graded nilradicals and their invariants
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-10T06%3A05%3A16IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Solvable%20Lie%20algebras%20with%20naturally%20graded%20nilradicals%20and%20their%20invariants&rft.jtitle=arXiv.org&rft.au=Ancochea,%20J%20M&rft.date=2006-02-01&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.0511027&rft_dat=%3Cproquest%3E2090040035%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2090040035&rft_id=info:pmid/&rfr_iscdi=true