{"id":"https://openalex.org/W7220950813","doi":"https://doi.org/10.48550/arxiv.2610.09868","title":"Ramified Quivers with Potentials, Monodromy Characters, and Cluster Bases I","display_name":"Ramified Quivers with Potentials, Monodromy Characters, and Cluster Bases I","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220950813","doi":"https://doi.org/10.48550/arxiv.2610.09868"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.09868","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09868","pdf_url":"https://arxiv.org/pdf/2610.09868","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/2610.09868","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072565036","display_name":"Jiarui Fei","orcid":"https://orcid.org/0000-0002-0053-2600","observed_orcids":["https://orcid.org/0000-0002-0053-2600"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Fei, Jiarui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5072565036"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9932000041007996,"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"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9932000041007996,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0017000000225380063,"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"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.0003000000142492354,"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/cluster-characters","display_name":"cluster characters","score":0.765999972820282},{"id":"https://openalex.org/keywords/jacobian-algebras","display_name":"Jacobian algebras","score":0.7639999985694885},{"id":"https://openalex.org/keywords/upper-cluster-algebras","display_name":"upper cluster algebras","score":0.7300000190734863},{"id":"https://openalex.org/keywords/newton-polytopes","display_name":"Newton polytopes","score":0.6050000190734863}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8514999747276306},{"id":"https://openalex.org/C96403706","wikidata":"https://www.wikidata.org/wiki/Q543956","display_name":"Monodromy","level":2,"score":0.830299973487854},{"id":"https://openalex.org/C165879259","wikidata":"https://www.wikidata.org/wiki/Q5136690","display_name":"Cluster algebra","level":3,"score":0.6746000051498413},{"id":"https://openalex.org/C168310172","wikidata":"https://www.wikidata.org/wiki/Q493980","display_name":"Quiver","level":2,"score":0.6428999900817871},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5134999752044678},{"id":"https://openalex.org/C2780311589","wikidata":"https://www.wikidata.org/wiki/Q6901559","display_name":"Monodromy matrix","level":3,"score":0.48399999737739563},{"id":"https://openalex.org/C104528550","wikidata":"https://www.wikidata.org/wiki/Q506265","display_name":"Triangular matrix","level":3,"score":0.46309998631477356},{"id":"https://openalex.org/C94863793","wikidata":"https://www.wikidata.org/wiki/Q1196652","display_name":"Exterior algebra","level":3,"score":0.43560001254081726},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.4156000018119812},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3935999870300293},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.38940000534057617},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.37400001287460327},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3569999933242798},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.33649998903274536},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.3084999918937683},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.29739999771118164},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2957000136375427},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.2888999879360199},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2612999975681305},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.2565000057220459},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.09868","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09868","pdf_url":"https://arxiv.org/pdf/2610.09868","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.2610.09868","doi":"https://doi.org/10.48550/arxiv.2610.09868","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.09868","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:2610.09868","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09868","pdf_url":"https://arxiv.org/pdf/2610.09868","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":[{"id":"https://openalex.org/G440546213","display_name":null,"funder_award_id":"12571038","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220950813.pdf","grobid_xml":"https://content.openalex.org/works/W7220950813.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1523097020","https://openalex.org/W1581840712","https://openalex.org/W1755464317","https://openalex.org/W1755641343","https://openalex.org/W1765882028","https://openalex.org/W1878406712","https://openalex.org/W1905777112","https://openalex.org/W1977307314","https://openalex.org/W2002007176","https://openalex.org/W2003878698","https://openalex.org/W2030944112","https://openalex.org/W2146870819","https://openalex.org/W2228651704","https://openalex.org/W2600446011","https://openalex.org/W2610506573","https://openalex.org/W2897909687","https://openalex.org/W2906511019","https://openalex.org/W2916768231","https://openalex.org/W2963483326","https://openalex.org/W2964022512","https://openalex.org/W2964070394","https://openalex.org/W2982399368","https://openalex.org/W3042172849","https://openalex.org/W3106950780","https://openalex.org/W3202317708","https://openalex.org/W4205214348","https://openalex.org/W4226100640","https://openalex.org/W4353083155","https://openalex.org/W4394766744","https://openalex.org/W4403586074","https://openalex.org/W4407683993","https://openalex.org/W4414940270","https://openalex.org/W7133624151","https://openalex.org/W7212127222"],"related_works":["https://openalex.org/W2237763061","https://openalex.org/W7098987383","https://openalex.org/W7099069003","https://openalex.org/W7098540706","https://openalex.org/W2002007176","https://openalex.org/W1977307314","https://openalex.org/W2085564384","https://openalex.org/W1669123188","https://openalex.org/W2782674479","https://openalex.org/W1532847231"],"abstract_inverted_index":{"We":[0],"construct":[1],"categorical":[2],"models":[3],"and":[4,67,109,135,150,159],"cluster":[5,9,111,125,138],"characters":[6,118],"for":[7,75,92,127],"skew-symmetrizable":[8],"algebras":[10,152],"admitting":[11],"good":[12,71,83],"ramified":[13],"realizations.":[14],"Goodness":[15],"is":[16,25,28,143,169],"equivalent":[17],"to":[18,30],"nondegenerate":[19,73,85],"realizability.":[20],"When":[21],"a":[22,70,82,98,120,155],"reddening":[23,55],"sequence":[24],"given,":[26],"it":[27],"enough":[29],"check":[31],"sign":[32],"coherence":[33],"of":[34,122,164,171],"the":[35,87,114,123,148,161,165,172],"arrow":[36],"types":[37,47],"along":[38],"that":[39],"sequence.":[40],"Triangular":[41],"extensions":[42,66],"with":[43,131],"arbitrary":[44,128],"connecting":[45],"bimodule":[46],"preserve":[48],"goodness":[49],"when":[50,147],"both":[51],"component":[52],"matrices":[53],"admit":[54],"sequences.":[56],"Consequently,":[57],"every":[58,76],"matrix":[59],"obtained":[60],"from":[61],"one":[62],"vertex":[63],"by":[64],"triangular":[65],"mutations":[68],"admits":[69],"Jacobi-finite":[72,84],"realization":[74],"compatible":[77],"positive":[78],"integral":[79],"symmetrizer.":[80],"For":[81,154],"realization,":[86],"monodromy":[88,167],"$F$-polynomials":[89],"satisfy":[90],"mutation":[91],"all":[93,137],"finite":[94],"decorated":[95],"representations,":[96],"without":[97],"rigidity":[99],"hypothesis.":[100],"A":[101],"full":[102],"initial":[103],"order":[104],"determines":[105],"valued":[106],"universal":[107],"presentations":[108],"their":[110],"characters.":[112],"Under":[113],"reachability":[115],"condition,":[116],"these":[117],"form":[119],"basis":[121,146],"middle":[124,149],"algebra":[126,158],"geometric":[129],"coefficients,":[130],"frozen":[132],"variables":[133],"inverted,":[134],"contain":[136],"monomials.":[139],"The":[140],"same":[141],"family":[142],"an":[144],"upper-cluster-algebra":[145],"upper":[151],"coincide.":[153],"fixed":[156],"Jacobian":[157],"$\u03b4$-vector,":[160],"Newton":[162],"polytope":[163],"generic":[166],"$F$-polynomial":[168],"independent":[170],"order.":[173]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-09T00:00:00"}