{"id":"https://openalex.org/W7125704695","doi":"https://doi.org/10.3390/axioms15010080","title":"Nijenhuis Operators on 2D Pre-Lie Algebras and 3D Associative Algebras","display_name":"Nijenhuis Operators on 2D Pre-Lie Algebras and 3D Associative Algebras","publication_year":2026,"publication_date":"2026-01-22","ids":{"openalex":"https://openalex.org/W7125704695","doi":"https://doi.org/10.3390/axioms15010080"},"language":"en","primary_location":{"id":"doi:10.3390/axioms15010080","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15010080","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/axioms15010080","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060771048","display_name":"Xiaoguang Zou","orcid":"https://orcid.org/0000-0002-8972-136X"},"institutions":[{"id":"https://openalex.org/I181679659","display_name":"Shanghai University of Finance and Economics","ror":"https://ror.org/00wtvfq62","country_code":"CN","type":"education","lineage":["https://openalex.org/I181679659"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoguang Zou","raw_affiliation_strings":["Zhejiang College, Shanghai University of Finance and Economics, Jinhua 321013, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhejiang College, Shanghai University of Finance and Economics, Jinhua 321013, China","institution_ids":["https://openalex.org/I181679659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123865680","display_name":"Xiang Gao","orcid":null},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiang Gao","raw_affiliation_strings":["School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China","institution_ids":["https://openalex.org/I135237710"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123874431","display_name":"Chuangchuang Kang","orcid":null},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chuangchuang Kang","raw_affiliation_strings":["School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China","institution_ids":["https://openalex.org/I135237710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5123872403","display_name":"Jiafeng L\u00fc","orcid":null},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiafeng L\u00fc","raw_affiliation_strings":["School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China"],"raw_orcid":"https://orcid.org/0000-0002-2637-142X","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China","institution_ids":["https://openalex.org/I135237710"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19048621,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"1","first_page":"80","last_page":"80"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9950000047683716,"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":0.9950000047683716,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.000699999975040555,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.0005000000237487257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.7206000089645386},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5426999926567078},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.45399999618530273},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.35839998722076416},{"id":"https://openalex.org/keywords/universal-enveloping-algebra","display_name":"Universal enveloping algebra","score":0.303600013256073}],"concepts":[{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.7206000089645386},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6035000085830688},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5426999926567078},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4580000042915344},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.45399999618530273},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.35839998722076416},{"id":"https://openalex.org/C155058155","wikidata":"https://www.wikidata.org/wiki/Q1673406","display_name":"Universal enveloping algebra","level":3,"score":0.303600013256073},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.24369999766349792},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.24250000715255737}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms15010080","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15010080","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3c2d433e3eb947529a1ce83dfa681b33","is_oa":true,"landing_page_url":"https://doaj.org/article/3c2d433e3eb947529a1ce83dfa681b33","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 15, Iss 1, p 80 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms15010080","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15010080","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5304043223","display_name":null,"funder_award_id":"12571042","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6317905538","display_name":null,"funder_award_id":"LZ25A010002","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320338464","display_name":"Natural Science Foundation of Zhejiang Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1511378139","https://openalex.org/W1544626381","https://openalex.org/W1829744333","https://openalex.org/W1975873151","https://openalex.org/W1976565614","https://openalex.org/W2025277274","https://openalex.org/W2035353115","https://openalex.org/W2040917591","https://openalex.org/W2070891992","https://openalex.org/W2070991255","https://openalex.org/W2163396252","https://openalex.org/W2232995269","https://openalex.org/W2271658455","https://openalex.org/W2346946956","https://openalex.org/W2798173719","https://openalex.org/W2954589742","https://openalex.org/W2996364632","https://openalex.org/W3138307302","https://openalex.org/W3165755765","https://openalex.org/W3206311950","https://openalex.org/W4387826622","https://openalex.org/W4388906633","https://openalex.org/W4415242014"],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,24],"describe":[4],"all":[5],"Nijenhuis":[6],"operators":[7],"on":[8,32],"2-dimensional":[9],"complex":[10,15],"pre-Lie":[11],"algebras":[12],"and":[13],"3-dimensional":[14],"associative":[16],"algebras.":[17,37],"As":[18],"an":[19],"application,":[20],"using":[21],"these":[22],"operators,":[23],"obtain":[25],"solutions":[26],"to":[27],"the":[28,33],"classical":[29],"Yang-Baxter":[30],"equation":[31],"corresponding":[34],"sub-adjacent":[35],"Lie":[36]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-01-27T00:00:00"}