{"id":"https://openalex.org/W4384616477","doi":"https://doi.org/10.3842/sigma.2026.110","title":"The Geometric Deformation of Curved $L_\\infty$ Algebras and Lie Algebroids","display_name":"The Geometric Deformation of Curved $L_\\infty$ Algebras and Lie Algebroids","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W4384616477","doi":"https://doi.org/10.3842/sigma.2026.110"},"language":"en","primary_location":{"id":"doi:10.3842/sigma.2026.110","doi":"https://doi.org/10.3842/sigma.2026.110","is_oa":true,"landing_page_url":"https://doi.org/10.3842/sigma.2026.110","pdf_url":"https://sigma-journal.com/2026/110/sigma26-110.pdf","source":{"id":"https://openalex.org/S190431191","display_name":"Symmetry Integrability and Geometry Methods and Applications","issn_l":"1815-0659","issn":["1815-0659"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-c","jufo-1","norway-1","oarl","poland-70","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310321802","host_organization_name":"National Academy of Sciences of Ukraine","host_organization_lineage":["https://openalex.org/P4310321802"],"host_organization_lineage_names":["National Academy of Sciences of Ukraine"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry, Integrability and Geometry: Methods and Applications","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sigma-journal.com/2026/110/sigma26-110.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067449363","display_name":"Xiaoyi Cui","orcid":"https://orcid.org/0009-0007-9099-0018","observed_orcids":["https://orcid.org/0009-0007-9099-0018"]},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaoyi Cui","raw_affiliation_strings":["Sun Yat-sen University, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sun Yat-sen University, P.R. China","institution_ids":["https://openalex.org/I157773358"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067449363"],"corresponding_institution_ids":["https://openalex.org/I157773358"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9771000146865845,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9771000146865845,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.016200000420212746,"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":0.004399999976158142,"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/geometric-deformation","display_name":"geometric deformation","score":0.8339999914169312},{"id":"https://openalex.org/keywords/lie-algebroids","display_name":"Lie algebroids","score":0.9769999980926514},{"id":"https://openalex.org/keywords/vector-bundles","display_name":"vector bundles","score":0.8429999947547913},{"id":"https://openalex.org/keywords/modular-class","display_name":"modular class","score":0.8939999938011169},{"id":"https://openalex.org/keywords/lie-algebroid-cohomology","display_name":"Lie algebroid cohomology","score":0.9700000286102295},{"id":"https://openalex.org/keywords/poisson-sigma-model","display_name":"Poisson sigma model","score":0.9210000038146973}],"concepts":[{"id":"https://openalex.org/C2776503324","wikidata":"https://www.wikidata.org/wiki/Q6543810","display_name":"Lie algebroid","level":3,"score":0.8707150220870972},{"id":"https://openalex.org/C95857938","wikidata":"https://www.wikidata.org/wiki/Q658429","display_name":"Vector bundle","level":2,"score":0.7161259651184082},{"id":"https://openalex.org/C151527765","wikidata":"https://www.wikidata.org/wiki/Q1069818","display_name":"Chern class","level":2,"score":0.6973937749862671},{"id":"https://openalex.org/C44594293","wikidata":"https://www.wikidata.org/wiki/Q1062978","display_name":"Characteristic class","level":3,"score":0.6855137348175049},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6705299019813538},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5945928692817688},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.581308901309967},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5446696281433105},{"id":"https://openalex.org/C204366326","wikidata":"https://www.wikidata.org/wiki/Q3027650","display_name":"Deformation (meteorology)","level":2,"score":0.5346989035606384},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.47698885202407837},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.4427781403064728},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3679090142250061},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20369285345077515},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.148758202791214},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07277897000312805},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3842/sigma.2026.110","doi":"https://doi.org/10.3842/sigma.2026.110","is_oa":true,"landing_page_url":"https://doi.org/10.3842/sigma.2026.110","pdf_url":"https://sigma-journal.com/2026/110/sigma26-110.pdf","source":{"id":"https://openalex.org/S190431191","display_name":"Symmetry Integrability and Geometry Methods and Applications","issn_l":"1815-0659","issn":["1815-0659"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-c","jufo-1","norway-1","oarl","poland-70","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310321802","host_organization_name":"National Academy of Sciences of Ukraine","host_organization_lineage":["https://openalex.org/P4310321802"],"host_organization_lineage_names":["National Academy of Sciences of Ukraine"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry, Integrability and Geometry: Methods and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2307.07497","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2307.07497","pdf_url":"https://arxiv.org/pdf/2307.07497","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2307.07497","doi":"https://doi.org/10.48550/arxiv.2307.07497","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2307.07497","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.3842/sigma.2026.110","doi":"https://doi.org/10.3842/sigma.2026.110","is_oa":true,"landing_page_url":"https://doi.org/10.3842/sigma.2026.110","pdf_url":"https://sigma-journal.com/2026/110/sigma26-110.pdf","source":{"id":"https://openalex.org/S190431191","display_name":"Symmetry Integrability and Geometry Methods and Applications","issn_l":"1815-0659","issn":["1815-0659"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-c","jufo-1","norway-1","oarl","poland-70","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310321802","host_organization_name":"National Academy of Sciences of Ukraine","host_organization_lineage":["https://openalex.org/P4310321802"],"host_organization_lineage_names":["National Academy of Sciences of Ukraine"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry, Integrability and Geometry: Methods and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321870","display_name":"Georg-August-Universit\u00e4t G\u00f6ttingen","ror":"https://ror.org/01y9bpm73"},{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4384616477.pdf","grobid_xml":"https://content.openalex.org/works/W4384616477.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1520607580","https://openalex.org/W1664654057","https://openalex.org/W1807973447","https://openalex.org/W1882455465","https://openalex.org/W1937059200","https://openalex.org/W1987511575","https://openalex.org/W2008218939","https://openalex.org/W2038555916","https://openalex.org/W2052250414","https://openalex.org/W2060588344","https://openalex.org/W2062621534","https://openalex.org/W2066212725","https://openalex.org/W2071417479","https://openalex.org/W2081733730","https://openalex.org/W2089223446","https://openalex.org/W2106817500","https://openalex.org/W2112257400","https://openalex.org/W2112885389","https://openalex.org/W2125623751","https://openalex.org/W2165142179","https://openalex.org/W2169107602","https://openalex.org/W2170184309","https://openalex.org/W2593618184","https://openalex.org/W2614196406","https://openalex.org/W2771361481","https://openalex.org/W2794437145","https://openalex.org/W2889733334","https://openalex.org/W2953096876","https://openalex.org/W3136899487","https://openalex.org/W3138025561","https://openalex.org/W3166333461","https://openalex.org/W4251023825","https://openalex.org/W4300001503","https://openalex.org/W4360982894"],"related_works":["https://openalex.org/W1815914269","https://openalex.org/W2034162903","https://openalex.org/W2801768622","https://openalex.org/W2903099868","https://openalex.org/W2271171338","https://openalex.org/W1665008591","https://openalex.org/W1748196613","https://openalex.org/W2082595641","https://openalex.org/W2342740083","https://openalex.org/W2962784596"],"abstract_inverted_index":{"While":[0],"$L_\\infty$":[1,35,64,160],"algebras":[2,65],"are":[3],"fundamental":[4],"structures":[5,18,83],"in":[6,16,99,111],"differential":[7],"geometry":[8],"and":[9,41,73],"mathematical":[10],"physics,":[11],"the":[12,24,93,100,108,116,122,128,138],"geometric":[13,48,60,139,157],"information":[14],"encoded":[15],"such":[17,44,76],"is":[19,97],"often":[20],"implicit.":[21],"We":[22],"address":[23],"following":[25],"question:":[26],"What":[27],"constitutes":[28],"a":[29,68,90,149],"geometrically":[30],"meaningful":[31],"deformation":[32],"of":[33,55,62,92,118,159],"an":[34],"algebra":[36],"arising":[37],"from":[38,67,156],"vector":[39,69],"bundles,":[40],"how":[42],"can":[43],"deformations":[45,61,77,140,158],"classify":[46],"new":[47],"invariants?":[49],"Inspired":[50],"by":[51],"nonabelian":[52],"extension":[53],"theory":[54],"Lie":[56,81,112,120],"algebras,":[57],"we":[58],"define":[59],"curved":[63],"constructed":[66],"bundle":[70],"$V\\to":[71],"M$,":[72],"demonstrate":[74],"that":[75,89,137],"uniquely":[78],"correspond":[79,126],"to":[80,127,133],"algebroid":[82,113],"on":[84],"$V$.":[85],"Explicit":[86],"computations":[87],"reveal":[88],"representative":[91],"first":[94],"Atiyah-Chern":[95,124],"class":[96,110],"exact":[98],"total":[101],"Weil":[102],"complex,":[103],"with":[104],"its":[105],"primitive":[106],"representing":[107],"modular":[109],"cohomology.":[114],"In":[115],"case":[117],"action":[119],"algebroids,":[121],"leading-order":[123],"classes":[125],"equivariant":[129],"Chern":[130],"characters.":[131],"Applications":[132],"BV":[134],"theories":[135,155],"show":[136],"naturally":[141],"generate":[142],"Poisson":[143],"sigma":[144],"models.":[145],"These":[146],"results":[147],"provide":[148],"coherent":[150],"framework":[151],"for":[152],"deriving":[153],"field":[154],"algebras.":[161]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2023-07-18T00:00:00"}