{"id":"https://openalex.org/W7203629814","doi":"https://doi.org/10.48550/arxiv.2608.13872","title":"$C_2$-Cofiniteness and Rationality of the Icosahedral Orbifold $V_{L_2}^{A_5}$","display_name":"$C_2$-Cofiniteness and Rationality of the Icosahedral Orbifold $V_{L_2}^{A_5}$","publication_year":2026,"publication_date":"2026-08-14","ids":{"openalex":"https://openalex.org/W7203629814","doi":"https://doi.org/10.48550/arxiv.2608.13872"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.13872","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13872","pdf_url":"https://arxiv.org/pdf/2608.13872","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"},"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/2608.13872","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147352673","display_name":"Shun Xu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xu, Shun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5147352673"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":4,"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":0.951200008392334,"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":0.951200008392334,"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/T10849","display_name":"Finite Group Theory Research","score":0.012600000016391277,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.004699999932199717,"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/rationality","display_name":"rationality","score":0.6359999775886536},{"id":"https://openalex.org/keywords/vertex-operator-algebras","display_name":"vertex operator algebras","score":0.8190000057220459},{"id":"https://openalex.org/keywords/lattice-vertex-operator-algebras","display_name":"lattice vertex operator algebras","score":0.8820000290870667}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7095999717712402},{"id":"https://openalex.org/C143782950","wikidata":"https://www.wikidata.org/wiki/Q40460","display_name":"Orbifold","level":2,"score":0.701200008392334},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6039999723434448},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.5813000202178955},{"id":"https://openalex.org/C113709186","wikidata":"https://www.wikidata.org/wiki/Q5986738","display_name":"Icosahedral symmetry","level":2,"score":0.5511000156402588},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.48910000920295715},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4860999882221222},{"id":"https://openalex.org/C179724543","wikidata":"https://www.wikidata.org/wiki/Q28509","display_name":"Vertex operator algebra","level":5,"score":0.4487999975681305},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4429999887943268},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4009999930858612},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35269999504089355},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3352999985218048},{"id":"https://openalex.org/C201717286","wikidata":"https://www.wikidata.org/wiki/Q938185","display_name":"Rationality","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.267300009727478},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.25850000977516174}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.13872","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13872","pdf_url":"https://arxiv.org/pdf/2608.13872","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.2608.13872","doi":"https://doi.org/10.48550/arxiv.2608.13872","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.13872","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":"pmh:oai:arXiv.org:2608.13872","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13872","pdf_url":"https://arxiv.org/pdf/2608.13872","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203629814.pdf","grobid_xml":"https://content.openalex.org/works/W7203629814.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2295005153","https://openalex.org/W2346789124"],"related_works":["https://openalex.org/W2006990927","https://openalex.org/W2002940388","https://openalex.org/W2762505894","https://openalex.org/W1580338134","https://openalex.org/W2022121630","https://openalex.org/W7214293616","https://openalex.org/W7096552524","https://openalex.org/W2128354726","https://openalex.org/W1772941714","https://openalex.org/W1622590165"],"abstract_inverted_index":{"Let":[0],"$L_2=\\mathbb{Z}\u03b1$":[1],"be":[2],"the":[3,14,30],"rank-one":[4],"root":[5],"lattice":[6,15],"with":[7],"$(\u03b1,\u03b1)=2$,":[8],"and":[9],"let":[10],"$A_5$":[11],"act":[12],"on":[13],"vertex":[16,32],"operator":[17,33],"algebra":[18,34],"$V_{L_2}$":[19],"through":[20],"an":[21],"icosahedral":[22],"subgroup":[23],"of":[24],"$\\operatorname{Aut}(V_{L_2})\\cong":[25],"PSL_2(\\mathbb{C})$.":[26],"We":[27],"prove":[28],"that":[29],"fixed-point":[31],"$V_{L_2}^{A_5}$":[35],"is":[36],"strongly":[37],"rational.":[38]},"counts_by_year":[{"year":2026,"cited_by_count":4}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-18T00:00:00"}