{"id":"https://openalex.org/W7207785400","doi":"https://doi.org/10.48550/arxiv.2609.02137","title":"An $\\mathfrak{sl}_2$-action on the uri Lie algebra","display_name":"An $\\mathfrak{sl}_2$-action on the uri Lie algebra","publication_year":2026,"publication_date":"2026-09-02","ids":{"openalex":"https://openalex.org/W7207785400","doi":"https://doi.org/10.48550/arxiv.2609.02137"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.02137","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02137","pdf_url":"https://arxiv.org/pdf/2609.02137","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/2609.02137","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076775755","display_name":"Henrik Bachmann","orcid":"https://orcid.org/0000-0003-0480-4375","observed_orcids":["https://orcid.org/0000-0003-0480-4375"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bachmann, Henrik","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5076775755"],"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/T11428","display_name":"Advanced Mathematical Identities","score":0.7554000020027161,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.7554000020027161,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.23170000314712524,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.0038999998942017555,"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/multiple-zeta-values","display_name":"multiple zeta values","score":0.8519999980926514},{"id":"https://openalex.org/keywords/lowering-operators","display_name":"lowering operators","score":0.781000018119812},{"id":"https://openalex.org/keywords/raising-operators","display_name":"raising operators","score":0.7329999804496765},{"id":"https://openalex.org/keywords/lie-subalgebras","display_name":"Lie subalgebras","score":0.621999979019165}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7692999839782715},{"id":"https://openalex.org/C73648015","wikidata":"https://www.wikidata.org/wiki/Q6543817","display_name":"Lie conformal algebra","level":3,"score":0.61080002784729},{"id":"https://openalex.org/C5475112","wikidata":"https://www.wikidata.org/wiki/Q632521","display_name":"Affine Lie algebra","level":4,"score":0.5569000244140625},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5126000046730042},{"id":"https://openalex.org/C155058155","wikidata":"https://www.wikidata.org/wiki/Q1673406","display_name":"Universal enveloping algebra","level":3,"score":0.512499988079071},{"id":"https://openalex.org/C144091092","wikidata":"https://www.wikidata.org/wiki/Q3611543","display_name":"Graded Lie algebra","level":3,"score":0.5019999742507935},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46889999508857727},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.42239999771118164},{"id":"https://openalex.org/C22365015","wikidata":"https://www.wikidata.org/wiki/Q1003162","display_name":"Simple Lie group","level":3,"score":0.3824000060558319},{"id":"https://openalex.org/C58910974","wikidata":"https://www.wikidata.org/wiki/Q1017106","display_name":"Adjoint representation","level":3,"score":0.3617999851703644},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.3612000048160553},{"id":"https://openalex.org/C78804095","wikidata":"https://www.wikidata.org/wiki/Q1133024","display_name":"Lie superalgebra","level":5,"score":0.33970001339912415},{"id":"https://openalex.org/C203946495","wikidata":"https://www.wikidata.org/wiki/Q1017106","display_name":"Adjoint representation of a Lie algebra","level":4,"score":0.32269999384880066},{"id":"https://openalex.org/C2778052762","wikidata":"https://www.wikidata.org/wiki/Q2366896","display_name":"Semisimple Lie algebra","level":5,"score":0.3197999894618988},{"id":"https://openalex.org/C186489112","wikidata":"https://www.wikidata.org/wiki/Q763735","display_name":"Representation of a Lie group","level":3,"score":0.31360000371932983},{"id":"https://openalex.org/C66411559","wikidata":"https://www.wikidata.org/wiki/Q5532440","display_name":"Generalized Kac\u2013Moody algebra","level":5,"score":0.30889999866485596},{"id":"https://openalex.org/C99634282","wikidata":"https://www.wikidata.org/wiki/Q634557","display_name":"Killing form","level":5,"score":0.29260000586509705},{"id":"https://openalex.org/C65096084","wikidata":"https://www.wikidata.org/wiki/Q2912114","display_name":"Cartan subalgebra","level":5,"score":0.2904999852180481},{"id":"https://openalex.org/C81999800","wikidata":"https://www.wikidata.org/wiki/Q1454725","display_name":"Current algebra","level":3,"score":0.2815000116825104},{"id":"https://openalex.org/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.2806999981403351},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27869999408721924},{"id":"https://openalex.org/C195592935","wikidata":"https://www.wikidata.org/wiki/Q4544947","display_name":"(g,K)-module","level":5,"score":0.2711000144481659},{"id":"https://openalex.org/C197273675","wikidata":"https://www.wikidata.org/wiki/Q13220368","display_name":"Representation theory","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C100899422","wikidata":"https://www.wikidata.org/wiki/Q5058347","display_name":"Cellular algebra","level":4,"score":0.265500009059906},{"id":"https://openalex.org/C174696410","wikidata":"https://www.wikidata.org/wiki/Q7301156","display_name":"Real form","level":5,"score":0.2653999924659729},{"id":"https://openalex.org/C169982404","wikidata":"https://www.wikidata.org/wiki/Q6543816","display_name":"Lie coalgebra","level":5,"score":0.26420000195503235},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.2574000060558319}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.02137","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02137","pdf_url":"https://arxiv.org/pdf/2609.02137","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.2609.02137","doi":"https://doi.org/10.48550/arxiv.2609.02137","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.02137","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:2609.02137","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02137","pdf_url":"https://arxiv.org/pdf/2609.02137","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7207785400.pdf","grobid_xml":"https://content.openalex.org/works/W7207785400.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W786027850","https://openalex.org/W3205931644","https://openalex.org/W4390306303","https://openalex.org/W4414790746","https://openalex.org/W6948212772","https://openalex.org/W7128483201"],"related_works":["https://openalex.org/W7214354665","https://openalex.org/W7214246046","https://openalex.org/W4415031036","https://openalex.org/W4394656705","https://openalex.org/W2085791502","https://openalex.org/W7119335435","https://openalex.org/W4416256368","https://openalex.org/W6910848258","https://openalex.org/W2142715794","https://openalex.org/W2144652714"],"abstract_inverted_index":{"We":[0,82],"construct":[1],"an":[2,102],"$\\mathfrak{sl}_2$-action":[3],"by":[4,101],"derivations":[5],"on":[6,79],"the":[7,18,29,53,63,70],"Lie":[8,26,40,58,85],"algebra":[9,27,41],"$\\mathfrak":[10,50,60,80,87,90],"B$":[11,61,91],"of":[12,21,52,66,89],"swap":[13],"invariant":[14],"alternil":[15],"bimoulds":[16],"with":[17],"uri":[19],"bracket":[20],"K\u00fchn":[22],"and":[23,73,92],"Schneps.":[24],"This":[25],"plays":[28,43],"role":[30],"for":[31,44],"formal":[32],"multiple":[33,45],"Eisenstein":[34],"series":[35],"which":[36],"Racinet's":[37],"double":[38],"shuffle":[39],"$\\mathfrak{dm}_0$":[42,99],"zeta":[46],"values.":[47],"The":[48],"kernel":[49],"m$":[51],"lowering":[54],"operator":[55],"is":[56,62,96],"a":[57,84],"subalgebra,":[59],"direct":[64],"sum":[65],"its":[67],"iterates":[68],"under":[69],"raising":[71],"operator,":[72],"this":[74],"gives":[75],"Rankin-Cohen":[76],"type":[77],"operators":[78],"m$.":[81],"define":[83],"subalgebra":[86],"d$":[88],"show":[93],"that":[94],"it":[95],"isomorphic":[97],"to":[98],"extended":[100],"additional":[103],"element":[104],"in":[105],"weight":[106],"one.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-04T00:00:00"}