{"id":"https://openalex.org/W7216467272","doi":"https://doi.org/10.48550/arxiv.2610.01556","title":"Local and 2 local $\\frac{1}{2}$-derivation of $n$-dimensional totally graded filiform Lie algebras","display_name":"Local and 2 local $\\frac{1}{2}$-derivation of $n$-dimensional totally graded filiform Lie algebras","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7216467272","doi":"https://doi.org/10.48550/arxiv.2610.01556"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.01556","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01556","pdf_url":"https://arxiv.org/pdf/2610.01556","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.01556","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036177570","display_name":"Farhodjon Arzikulov","orcid":"https://orcid.org/0000-0002-1669-6474","observed_orcids":["https://orcid.org/0000-0002-1669-6474"]},"institutions":[{"id":"https://openalex.org/I1300976906","display_name":"Andijan State University","ror":"https://ror.org/00bad4666","country_code":"UZ","type":"education","lineage":["https://openalex.org/I1300976906"]},{"id":"https://openalex.org/I1302269238","display_name":"Academy of Sciences Republic of Uzbekistan","ror":"https://ror.org/01xgfaw76","country_code":"UZ","type":"government","lineage":["https://openalex.org/I1302269238","https://openalex.org/I4405266844"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Arzikulov, Farkhodzhon","raw_affiliation_strings":["Mathematics , Andijan State University , University 129 , Andijan , 170100 , Uzbekistan","V.I. Romanovskiy Institute of Mathematics , Uzbekistan Academy of Sciences , Olmazor district , University street 9 , Tashkent , 100174 , Uzbekistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics , Andijan State University , University 129 , Andijan , 170100 , Uzbekistan","institution_ids":["https://openalex.org/I1300976906"]},{"raw_affiliation_string":"V.I. Romanovskiy Institute of Mathematics , Uzbekistan Academy of Sciences , Olmazor district , University street 9 , Tashkent , 100174 , Uzbekistan","institution_ids":["https://openalex.org/I1302269238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5143765925","display_name":"Mirzobek Shodiev","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3131790217","display_name":"Bukhara State University","ror":"https://ror.org/05k4xnj24","country_code":"UZ","type":"education","lineage":["https://openalex.org/I3131790217"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Shodiev, Mirzobek","raw_affiliation_strings":["Mathematics , Bukhara State University , Mirzo Iqbol street 11 , Bukhara , 160107 , Uzbekistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics , Bukhara State University , Mirzo Iqbol street 11 , Bukhara , 160107 , Uzbekistan","institution_ids":["https://openalex.org/I3131790217"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":1.0,"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":1.0,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.0,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homogeneous-functions","display_name":"homogeneous functions","score":0.49799999594688416},{"id":"https://openalex.org/keywords/structural-sequence","display_name":"structural sequence","score":0.47999998927116394},{"id":"https://openalex.org/keywords/local-rigidity","display_name":"local rigidity","score":0.6460000276565552}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8216000199317932},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6049000024795532},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.527400016784668},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.5098999738693237},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4982999861240387},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.45500001311302185},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.44609999656677246},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.4083000123500824},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39070001244544983},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.38109999895095825},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.3488999903202057},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.3319999873638153},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.3276999890804291},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.3260999917984009},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.30489999055862427},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29420000314712524},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C77170095","wikidata":"https://www.wikidata.org/wiki/Q1753188","display_name":"Linearity","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C2986090443","wikidata":"https://www.wikidata.org/wiki/Q77870413","display_name":"Local structure","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.262800008058548}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.01556","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01556","pdf_url":"https://arxiv.org/pdf/2610.01556","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.01556","doi":"https://doi.org/10.48550/arxiv.2610.01556","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.01556","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.01556","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01556","pdf_url":"https://arxiv.org/pdf/2610.01556","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7216467272.pdf","grobid_xml":"https://content.openalex.org/works/W7216467272.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4402509501","https://openalex.org/W7171526459"],"related_works":["https://openalex.org/W4416670698","https://openalex.org/W7220713709","https://openalex.org/W4413932991","https://openalex.org/W4392742645","https://openalex.org/W7171526459","https://openalex.org/W4401051445","https://openalex.org/W7164735929","https://openalex.org/W3005242159","https://openalex.org/W7155057674","https://openalex.org/W7123575665"],"abstract_inverted_index":{"This":[0],"article":[1],"provides":[2],"a":[3],"complete":[4],"algebraic":[5],"description":[6],"of":[7,22,42,83,99,106,129],"$\\frac{1}{2}$-derivations,":[8,10],"local":[9,69,84,146],"and":[11,56,81,121],"2-local":[12,123],"$\\frac{1}{2}$-derivations":[13,43,124],"on":[14,26],"$n$-dimensional":[15],"totally":[16],"graded":[17],"complex":[18],"filiform":[19],"Lie":[20],"algebras":[21],"maximum":[23],"length.":[24],"Based":[25],"the":[27,39,45,57,67,78,91,96,100,126,142],"foundational":[28],"classification":[29],"framework":[30],"established":[31],"by":[32],"Janez":[33],"Bernik":[34],"(2020),":[35],"we":[36,76,88,116],"systematically":[37],"determine":[38],"vector":[40],"spaces":[41],"for":[44],"six":[46],"infinite":[47],"structural":[48,79],"sequences":[49],"($m_0(n)$,":[50],"$m_2(n)$,":[51],"$W^+(n)$,":[52],"$m_{0,1}(n)$,":[53],"$m_{0,2}(n)$,":[54],"$m_{0,3}(n)$)":[55],"five":[58],"exceptional":[59],"one-parameter":[60],"families":[61],"($g_{7,\u03b1}$":[62],"through":[63],"$g_{11,\u03b1}$).":[64],"By":[65],"analyzing":[66],"pointwise":[68],"evaluation":[70],"equations":[71],"via":[72],"parametric":[73],"matrix":[74],"systems,":[75],"establish":[77],"linearity":[80,110],"rigidity":[82,147],"$\\frac{1}{2}$-derivations.":[85],"In":[86],"contrast,":[87],"demonstrate":[89],"that":[90],"independent":[92],"parameters":[93],"residing":[94],"in":[95],"boundary":[97,114,144],"rows":[98],"$\\frac{1}{2}$-derivation":[101],"matrices":[102],"provide":[103],"sufficient":[104],"degrees":[105],"freedom":[107],"to":[108],"bypass":[109],"constraints.":[111],"Exploiting":[112],"these":[113],"configurations,":[115],"explicitly":[117],"construct":[118],"pure":[119],"non-linear":[120],"non-additive":[122],"leveraging":[125],"homogeneous":[127],"function":[128],"degree":[130],"one,":[131],"$f(z_1,":[132],"z_2)":[133],"=":[134],"z_1^3":[135],"/":[136],"(z_1^2":[137],"+":[138],"z_2^2)$,":[139],"thereby":[140],"defining":[141],"exact":[143],"where":[145],"fails.":[148]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}