{"id":"https://openalex.org/W7204755340","doi":"https://doi.org/10.1007/s11587-026-01179-5","title":"Local and 2-local $$\\frac{1}{2}$$-derivations on model and solvable Lie algebras with model nilradical","display_name":"Local and 2-local $$\\frac{1}{2}$$-derivations on model and solvable Lie algebras with model nilradical","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204755340","doi":"https://doi.org/10.1007/s11587-026-01179-5"},"language":"en","primary_location":{"id":"doi:10.1007/s11587-026-01179-5","doi":"https://doi.org/10.1007/s11587-026-01179-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11587-026-01179-5","pdf_url":null,"source":{"id":"https://openalex.org/S141413535","display_name":"Ricerche di Matematica","issn_l":"0035-5038","issn":["0035-5038","1827-3491"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ricerche di Matematica","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119007589","display_name":"Khusainboy Atajonov","orcid":"https://orcid.org/0009-0004-7175-5504","observed_orcids":["https://orcid.org/0009-0004-7175-5504"]},"institutions":[{"id":"https://openalex.org/I47151758","display_name":"National University of Uzbekistan","ror":"https://ror.org/011647w73","country_code":"UZ","type":"education","lineage":["https://openalex.org/I47151758"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Khusainboy Atajonov","raw_affiliation_strings":["National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, Uzbekistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, Uzbekistan","institution_ids":["https://openalex.org/I47151758"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072046944","display_name":"\u041d\u0430\u0444\u043e\u0441\u0430\u0442 \u0417\u0430\u043a\u0438\u0440\u0436\u0430\u043d\u043e\u0432\u043d\u0430 \u0412\u0430\u0438\u0441\u043e\u0432\u0430","orcid":"https://orcid.org/0009-0007-8191-5104","observed_orcids":["https://orcid.org/0009-0007-8191-5104"]},"institutions":[{"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":"Nafosat Vaisova","raw_affiliation_strings":["V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan","institution_ids":["https://openalex.org/I1302269238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035666167","display_name":"Bakhtiyor Yusupov","orcid":"https://orcid.org/0000-0001-9400-5811","observed_orcids":["https://orcid.org/0000-0001-9400-5811"]},"institutions":[{"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"]},{"id":"https://openalex.org/I14916453","display_name":"Urgench State University","ror":"https://ror.org/0593kfr97","country_code":"UZ","type":"education","lineage":["https://openalex.org/I14916453"]}],"countries":["UZ"],"is_corresponding":true,"raw_author_name":"Bakhtiyor Yusupov","raw_affiliation_strings":["Department of Algebra and Mathematical Engineering, Urgench State University, H. Alimdjan street, 14, 220100, Urgench, Uzbekistan","V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Algebra and Mathematical Engineering, Urgench State University, H. Alimdjan street, 14, 220100, Urgench, Uzbekistan","institution_ids":["https://openalex.org/I14916453"]},{"raw_affiliation_string":"V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan","institution_ids":["https://openalex.org/I1302269238"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035666167"],"corresponding_institution_ids":["https://openalex.org/I1302269238","https://openalex.org/I14916453"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":null,"fwci":6.8826,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.96943542,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":96},"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/solvable-lie-algebras","display_name":"solvable Lie algebras","score":0.9700000286102295},{"id":"https://openalex.org/keywords/nilradical","display_name":"nilradical","score":0.9369999766349792},{"id":"https://openalex.org/keywords/solvable-extensions","display_name":"solvable extensions","score":0.6840000152587891},{"id":"https://openalex.org/keywords/rigidity","display_name":"rigidity","score":0.7289999723434448},{"id":"https://openalex.org/keywords/complementary-space","display_name":"complementary space","score":0.5049999952316284},{"id":"https://openalex.org/keywords/lie-algebra-derivations","display_name":"Lie algebra derivations","score":0.7379999756813049}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8676000237464905},{"id":"https://openalex.org/C203946495","wikidata":"https://www.wikidata.org/wiki/Q1017106","display_name":"Adjoint representation of a Lie algebra","level":4,"score":0.7102000117301941},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.6233999729156494},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5888000130653381},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.5751000046730042},{"id":"https://openalex.org/C186489112","wikidata":"https://www.wikidata.org/wiki/Q763735","display_name":"Representation of a Lie group","level":3,"score":0.5375999808311462},{"id":"https://openalex.org/C22365015","wikidata":"https://www.wikidata.org/wiki/Q1003162","display_name":"Simple Lie group","level":3,"score":0.4675000011920929},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.4487000107765198},{"id":"https://openalex.org/C73648015","wikidata":"https://www.wikidata.org/wiki/Q6543817","display_name":"Lie conformal algebra","level":3,"score":0.4480000138282776},{"id":"https://openalex.org/C518143113","wikidata":"https://www.wikidata.org/wiki/Q4391941","display_name":"Non-associative algebra","level":4,"score":0.4318999946117401},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4239000082015991},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.41519999504089355},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3833000063896179},{"id":"https://openalex.org/C99634282","wikidata":"https://www.wikidata.org/wiki/Q634557","display_name":"Killing form","level":5,"score":0.3774000108242035},{"id":"https://openalex.org/C206219070","wikidata":"https://www.wikidata.org/wiki/Q1755242","display_name":"Nilpotent group","level":3,"score":0.3723999857902527},{"id":"https://openalex.org/C58910974","wikidata":"https://www.wikidata.org/wiki/Q1017106","display_name":"Adjoint representation","level":3,"score":0.35040000081062317},{"id":"https://openalex.org/C143135876","wikidata":"https://www.wikidata.org/wiki/Q357300","display_name":"Lie theory","level":5,"score":0.3476000130176544},{"id":"https://openalex.org/C188440111","wikidata":"https://www.wikidata.org/wiki/Q5062152","display_name":"Central series","level":4,"score":0.3449999988079071},{"id":"https://openalex.org/C5475112","wikidata":"https://www.wikidata.org/wiki/Q632521","display_name":"Affine Lie algebra","level":4,"score":0.32109999656677246},{"id":"https://openalex.org/C144091092","wikidata":"https://www.wikidata.org/wiki/Q3611543","display_name":"Graded Lie algebra","level":3,"score":0.2786000072956085},{"id":"https://openalex.org/C5106717","wikidata":"https://www.wikidata.org/wiki/Q3427416","display_name":"Fundamental representation","level":4,"score":0.2775000035762787}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11587-026-01179-5","doi":"https://doi.org/10.1007/s11587-026-01179-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11587-026-01179-5","pdf_url":null,"source":{"id":"https://openalex.org/S141413535","display_name":"Ricerche di Matematica","issn_l":"0035-5038","issn":["0035-5038","1827-3491"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ricerche di Matematica","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1558646683","https://openalex.org/W1814391638","https://openalex.org/W1840231702","https://openalex.org/W1980926949","https://openalex.org/W2012475157","https://openalex.org/W2045070762","https://openalex.org/W2065684900","https://openalex.org/W2085484777","https://openalex.org/W2177530975","https://openalex.org/W2317713845","https://openalex.org/W2791604259","https://openalex.org/W3010795971","https://openalex.org/W3175726526","https://openalex.org/W4213378330","https://openalex.org/W4214884226","https://openalex.org/W4248521801","https://openalex.org/W4309764899","https://openalex.org/W4390690923","https://openalex.org/W4392742645","https://openalex.org/W4396703009","https://openalex.org/W4412479210","https://openalex.org/W4413798178","https://openalex.org/W4413862865","https://openalex.org/W4413932991","https://openalex.org/W4416670698","https://openalex.org/W7123575665"],"related_works":["https://openalex.org/W4401051445","https://openalex.org/W7123575665","https://openalex.org/W4413862865","https://openalex.org/W2791604259","https://openalex.org/W4412479210","https://openalex.org/W2984979751","https://openalex.org/W4214884226","https://openalex.org/W6948566762","https://openalex.org/W2356560110","https://openalex.org/W2012475157"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-09-01T00:00:00"}