Naturally graded Lie algebras of slow growth

A pro-nilpotent Lie algebra is said to be naturally graded if it is isomorphic to its associated graded Lie algebra with respect to the filtration by the ideals in the lower central series. Finite-dimensional naturally graded Lie algebras are known in sub-Riemannian geometry and geometric control th...

Full description

Saved in:
Bibliographic Details
Published in:Sbornik. Mathematics 2019-06, Vol.210 (6), p.862-909
Main Author: Millionshchikov, D. V.
Format: Article
Language:English
Subjects:
Algebra
automorphism
Carnot algebra
central extension
Control theory
graded Lie algebra
Kac-Moody algebras
Lie groups
Series (mathematics)
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c278t-7045be81dc2212b2063fa516bb43cab87114b54f468d49619270c8b5c3e16c123
cites cdi_FETCH-LOGICAL-c278t-7045be81dc2212b2063fa516bb43cab87114b54f468d49619270c8b5c3e16c123
container_end_page 909
container_issue 6
container_start_page 862
container_title Sbornik. Mathematics
container_volume 210
creator Millionshchikov, D. V.
description A pro-nilpotent Lie algebra is said to be naturally graded if it is isomorphic to its associated graded Lie algebra with respect to the filtration by the ideals in the lower central series. Finite-dimensional naturally graded Lie algebras are known in sub-Riemannian geometry and geometric control theory, where they are called Carnot algebras. We classify the finite-dimensional and infinite-dimensional naturally graded Lie algebras with the property An arbitrary Lie algebra of this class is generated by the two- dimensional subspace , and the corresponding growth function satisfies the bound . Bibliography: 32 titles.
doi_str_mv 10.1070/SM9055
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1070_SM9055</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2357589765</sourcerecordid><originalsourceid>FETCH-LOGICAL-c278t-7045be81dc2212b2063fa516bb43cab87114b54f468d49619270c8b5c3e16c123</originalsourceid><addsrcrecordid>eNpdkEtLxDAUhYMoOI76G4qCK6v3pnl1KcP4gKoLdV2SNB07VDMmLcP8eyMVBFf3wP0453AIOUW4QpBw_fJYAud7ZIZMqJwpoPtJg2A5FygOyVGMawDgFNWMXD7pYQy673fZKujGNVnVuUz3K2eCjplvs9j7bfr57fB-TA5a3Ud38nvn5O12-bq4z6vnu4fFTZVbKtWQS2DcOIWNpRSpoSCKVnMUxrDCaqMkIjOctalew0qBJZVgleG2cCgs0mJOziffTfBfo4tDvfZj-EyRNS245KqUgifqYqJs8DEG19ab0H3osKsR6p8l6mmJBJ5NYOc3f07_oG9l5VgA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2357589765</pqid></control><display><type>article</type><title>Naturally graded Lie algebras of slow growth</title><source>Institute of Physics:Jisc Collections:IOP Publishing Read and Publish 2024-2025 (Reading List)</source><creator>Millionshchikov, D. V.</creator><creatorcontrib>Millionshchikov, D. V.</creatorcontrib><description>A pro-nilpotent Lie algebra is said to be naturally graded if it is isomorphic to its associated graded Lie algebra with respect to the filtration by the ideals in the lower central series. Finite-dimensional naturally graded Lie algebras are known in sub-Riemannian geometry and geometric control theory, where they are called Carnot algebras. We classify the finite-dimensional and infinite-dimensional naturally graded Lie algebras with the property An arbitrary Lie algebra of this class is generated by the two- dimensional subspace , and the corresponding growth function satisfies the bound . Bibliography: 32 titles.</description><identifier>ISSN: 1064-5616</identifier><identifier>EISSN: 1468-4802</identifier><identifier>DOI: 10.1070/SM9055</identifier><language>eng</language><publisher>Providence: London Mathematical Society, Turpion Ltd and the Russian Academy of Sciences</publisher><subject>Algebra ; automorphism ; Carnot algebra ; central extension ; Control theory ; graded Lie algebra ; Kac-Moody algebras ; Lie groups ; Series (mathematics)</subject><ispartof>Sbornik. Mathematics, 2019-06, Vol.210 (6), p.862-909</ispartof><rights>2019 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.</rights><rights>Copyright IOP Publishing Jun 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c278t-7045be81dc2212b2063fa516bb43cab87114b54f468d49619270c8b5c3e16c123</citedby><cites>FETCH-LOGICAL-c278t-7045be81dc2212b2063fa516bb43cab87114b54f468d49619270c8b5c3e16c123</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27922,27923</link.rule.ids></links><search><creatorcontrib>Millionshchikov, D. V.</creatorcontrib><title>Naturally graded Lie algebras of slow growth</title><title>Sbornik. Mathematics</title><addtitle>MSB</addtitle><addtitle>Sb. Math</addtitle><description>A pro-nilpotent Lie algebra is said to be naturally graded if it is isomorphic to its associated graded Lie algebra with respect to the filtration by the ideals in the lower central series. Finite-dimensional naturally graded Lie algebras are known in sub-Riemannian geometry and geometric control theory, where they are called Carnot algebras. We classify the finite-dimensional and infinite-dimensional naturally graded Lie algebras with the property An arbitrary Lie algebra of this class is generated by the two- dimensional subspace , and the corresponding growth function satisfies the bound . Bibliography: 32 titles.</description><subject>Algebra</subject><subject>automorphism</subject><subject>Carnot algebra</subject><subject>central extension</subject><subject>Control theory</subject><subject>graded Lie algebra</subject><subject>Kac-Moody algebras</subject><subject>Lie groups</subject><subject>Series (mathematics)</subject><issn>1064-5616</issn><issn>1468-4802</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNpdkEtLxDAUhYMoOI76G4qCK6v3pnl1KcP4gKoLdV2SNB07VDMmLcP8eyMVBFf3wP0453AIOUW4QpBw_fJYAud7ZIZMqJwpoPtJg2A5FygOyVGMawDgFNWMXD7pYQy673fZKujGNVnVuUz3K2eCjplvs9j7bfr57fB-TA5a3Ud38nvn5O12-bq4z6vnu4fFTZVbKtWQS2DcOIWNpRSpoSCKVnMUxrDCaqMkIjOctalew0qBJZVgleG2cCgs0mJOziffTfBfo4tDvfZj-EyRNS245KqUgifqYqJs8DEG19ab0H3osKsR6p8l6mmJBJ5NYOc3f07_oG9l5VgA</recordid><startdate>20190601</startdate><enddate>20190601</enddate><creator>Millionshchikov, D. V.</creator><general>London Mathematical Society, Turpion Ltd and the Russian Academy of Sciences</general><general>IOP Publishing</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>7U5</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>KR7</scope><scope>L7M</scope></search><sort><creationdate>20190601</creationdate><title>Naturally graded Lie algebras of slow growth</title><author>Millionshchikov, D. V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c278t-7045be81dc2212b2063fa516bb43cab87114b54f468d49619270c8b5c3e16c123</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Algebra</topic><topic>automorphism</topic><topic>Carnot algebra</topic><topic>central extension</topic><topic>Control theory</topic><topic>graded Lie algebra</topic><topic>Kac-Moody algebras</topic><topic>Lie groups</topic><topic>Series (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Millionshchikov, D. V.</creatorcontrib><collection>CrossRef</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Sbornik. Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Millionshchikov, D. V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Naturally graded Lie algebras of slow growth</atitle><jtitle>Sbornik. Mathematics</jtitle><stitle>MSB</stitle><addtitle>Sb. Math</addtitle><date>2019-06-01</date><risdate>2019</risdate><volume>210</volume><issue>6</issue><spage>862</spage><epage>909</epage><pages>862-909</pages><issn>1064-5616</issn><eissn>1468-4802</eissn><abstract>A pro-nilpotent Lie algebra is said to be naturally graded if it is isomorphic to its associated graded Lie algebra with respect to the filtration by the ideals in the lower central series. Finite-dimensional naturally graded Lie algebras are known in sub-Riemannian geometry and geometric control theory, where they are called Carnot algebras. We classify the finite-dimensional and infinite-dimensional naturally graded Lie algebras with the property An arbitrary Lie algebra of this class is generated by the two- dimensional subspace , and the corresponding growth function satisfies the bound . Bibliography: 32 titles.</abstract><cop>Providence</cop><pub>London Mathematical Society, Turpion Ltd and the Russian Academy of Sciences</pub><doi>10.1070/SM9055</doi><tpages>48</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1064-5616
ispartof Sbornik. Mathematics, 2019-06, Vol.210 (6), p.862-909
issn 1064-5616
1468-4802
language eng
recordid cdi_crossref_primary_10_1070_SM9055
source Institute of Physics:Jisc Collections:IOP Publishing Read and Publish 2024-2025 (Reading List)
subjects Algebra
automorphism
Carnot algebra
central extension
Control theory
graded Lie algebra
Kac-Moody algebras
Lie groups
Series (mathematics)
title Naturally graded Lie algebras of slow growth
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-14T11%3A32%3A38IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Naturally%20graded%20Lie%20algebras%20of%20slow%20growth&rft.jtitle=Sbornik.%20Mathematics&rft.au=Millionshchikov,%20D.%20V.&rft.date=2019-06-01&rft.volume=210&rft.issue=6&rft.spage=862&rft.epage=909&rft.pages=862-909&rft.issn=1064-5616&rft.eissn=1468-4802&rft_id=info:doi/10.1070/SM9055&rft_dat=%3Cproquest_cross%3E2357589765%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c278t-7045be81dc2212b2063fa516bb43cab87114b54f468d49619270c8b5c3e16c123%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2357589765&rft_id=info:pmid/&rfr_iscdi=true