{"id":"https://openalex.org/W4377138953","doi":"https://doi.org/10.3390/sym15051115","title":"Study on Poisson Algebra and Automorphism of a Special Class of Solvable Lie Algebras","display_name":"Study on Poisson Algebra and Automorphism of a Special Class of Solvable Lie Algebras","publication_year":2023,"publication_date":"2023-05-19","ids":{"openalex":"https://openalex.org/W4377138953","doi":"https://doi.org/10.3390/sym15051115"},"language":"en","primary_location":{"id":"doi:10.3390/sym15051115","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051115","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1115/pdf?version=1684734490","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/5/1115/pdf?version=1684734490","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053648239","display_name":"YU Demin","orcid":null},"institutions":[{"id":"https://openalex.org/I100286613","display_name":"Hunan Institute of Science and Technology","ror":"https://ror.org/044ysd349","country_code":"CN","type":"education","lineage":["https://openalex.org/I100286613"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Demin Yu","raw_affiliation_strings":["School of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China","institution_ids":["https://openalex.org/I100286613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102514708","display_name":"Chan Jiang","orcid":null},"institutions":[{"id":"https://openalex.org/I100286613","display_name":"Hunan Institute of Science and Technology","ror":"https://ror.org/044ysd349","country_code":"CN","type":"education","lineage":["https://openalex.org/I100286613"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chan Jiang","raw_affiliation_strings":["School of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China","institution_ids":["https://openalex.org/I100286613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102514709","display_name":"Jiejing Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I100286613","display_name":"Hunan Institute of Science and Technology","ror":"https://ror.org/044ysd349","country_code":"CN","type":"education","lineage":["https://openalex.org/I100286613"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiejing Ma","raw_affiliation_strings":["School of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China","institution_ids":["https://openalex.org/I100286613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053648239"],"corresponding_institution_ids":["https://openalex.org/I100286613"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":1.3052,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.74537037,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"15","issue":"5","first_page":"1115","last_page":"1115"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9871000051498413,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7938190698623657},{"id":"https://openalex.org/keywords/inner-automorphism","display_name":"Inner automorphism","score":0.626196026802063},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.5884461998939514},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5580358505249023},{"id":"https://openalex.org/keywords/lie-conformal-algebra","display_name":"Lie conformal algebra","score":0.5039476752281189},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.501701831817627},{"id":"https://openalex.org/keywords/lie-superalgebra","display_name":"Lie superalgebra","score":0.42329761385917664},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.41324058175086975},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.41162213683128357},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35559701919555664},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3480764329433441},{"id":"https://openalex.org/keywords/affine-lie-algebra","display_name":"Affine Lie algebra","score":0.27262479066848755},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.2460642158985138},{"id":"https://openalex.org/keywords/current-algebra","display_name":"Current algebra","score":0.1453167200088501},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.052605658769607544}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7938190698623657},{"id":"https://openalex.org/C124453015","wikidata":"https://www.wikidata.org/wiki/Q1139583","display_name":"Inner automorphism","level":4,"score":0.626196026802063},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.5884461998939514},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5580358505249023},{"id":"https://openalex.org/C73648015","wikidata":"https://www.wikidata.org/wiki/Q6543817","display_name":"Lie conformal algebra","level":3,"score":0.5039476752281189},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.501701831817627},{"id":"https://openalex.org/C78804095","wikidata":"https://www.wikidata.org/wiki/Q1133024","display_name":"Lie superalgebra","level":5,"score":0.42329761385917664},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.41324058175086975},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.41162213683128357},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35559701919555664},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3480764329433441},{"id":"https://openalex.org/C5475112","wikidata":"https://www.wikidata.org/wiki/Q632521","display_name":"Affine Lie algebra","level":4,"score":0.27262479066848755},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.2460642158985138},{"id":"https://openalex.org/C81999800","wikidata":"https://www.wikidata.org/wiki/Q1454725","display_name":"Current algebra","level":3,"score":0.1453167200088501},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.052605658769607544},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15051115","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051115","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1115/pdf?version=1684734490","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ec5bba6205fb4f86a95dbd4ecce8da25","is_oa":false,"landing_page_url":"https://doaj.org/article/ec5bba6205fb4f86a95dbd4ecce8da25","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 5, p 1115 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/5/1115/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15051115","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15051115","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051115","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1115/pdf?version=1684734490","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.699999988079071,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4377138953.pdf","grobid_xml":"https://content.openalex.org/works/W4377138953.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1166614230","https://openalex.org/W1975824997","https://openalex.org/W1984409840","https://openalex.org/W2005579419","https://openalex.org/W2016502988","https://openalex.org/W2016793511","https://openalex.org/W2028541610","https://openalex.org/W2046900284","https://openalex.org/W2065338978","https://openalex.org/W2088540134","https://openalex.org/W2133779877","https://openalex.org/W2166772305","https://openalex.org/W2352282176","https://openalex.org/W2359052533","https://openalex.org/W2474569623","https://openalex.org/W2962996842","https://openalex.org/W2963329255","https://openalex.org/W2963400927","https://openalex.org/W2964074280","https://openalex.org/W2973727626","https://openalex.org/W3101678304","https://openalex.org/W6995801439","https://openalex.org/W7042397105"],"related_works":["https://openalex.org/W2255396244","https://openalex.org/W2496242945","https://openalex.org/W2037605869","https://openalex.org/W2136606221","https://openalex.org/W2313746865","https://openalex.org/W2792426092","https://openalex.org/W4245623741","https://openalex.org/W4298307919","https://openalex.org/W4300561970","https://openalex.org/W2805639267"],"abstract_inverted_index":{"We":[0,55,68,106],"define":[1],"a":[2,29,43,51,101],"four-dimensional":[3],"Lie":[4,15,30,82],"algebra":[5,16],"g":[6,27,63],"in":[7],"this":[8,14,79],"paper":[9],"and":[10,47,72,84,114],"then":[11],"prove":[12],"that":[13,26,33],"is":[17,28,42,49,100],"solvable":[18],"but":[19],"not":[20],"nilpotent.":[21],"Due":[22],"to":[23],"the":[24,35,57,65,70,76,86,117],"fact":[25],"algebra,":[31],"\u2200x,y\u2208g,[x,y]=\u2212[y,x],":[32],"is,":[34],"operation":[36],"[,]":[37],"has":[38],"anti":[39],"symmetry.":[40],"Symmetry":[41],"very":[44,52],"important":[45,53],"law,":[46],"antisymmetry":[48],"also":[50],"law.":[54],"studied":[56,69,116],"structure":[58],"of":[59,78,81,88,104,110,119],"Poisson":[60],"algebras":[61],"on":[62],"using":[64],"matrix":[66],"method.":[67],"necessary":[71],"sufficient":[73],"conditions":[74],"for":[75],"automorphism":[77,90,112],"class":[80],"algebras,":[83],"give":[85,107],"decomposition":[87],"its":[89],"group":[91,113],"by":[92],"Aut(g)=G3G1G2G3G4G7G8G5,":[93],"or":[94,96],"Aut(g)=G3G1G2G3G4G7G8G5G6,":[95],"Aut(g)=G3G1G2G3G4G7G8G5G3,":[97],"where":[98],"Gi":[99],"commutative":[102],"subgroup":[103],"Aut(g).":[105],"some":[108],"subgroups":[109],"g\u2019s":[111],"systematically":[115],"properties":[118],"these":[120],"subgroups.":[121]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
