{"id":"https://openalex.org/W7223126207","doi":"https://doi.org/10.48550/arxiv.2610.28113","title":"Real Nullstellensatz for nilpotent Lie algebras","display_name":"Real Nullstellensatz for nilpotent Lie algebras","publication_year":2026,"publication_date":"2026-10-20","ids":{"openalex":"https://openalex.org/W7223126207","doi":"https://doi.org/10.48550/arxiv.2610.28113"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.28113","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28113","pdf_url":"https://arxiv.org/pdf/2610.28113","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/2610.28113","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103202167","display_name":"Philipp Schmitt","orcid":"https://orcid.org/0000-0003-4058-0946","observed_orcids":["https://orcid.org/0000-0003-4058-0946"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schmitt, Philipp","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5048568387","display_name":"Matthias Sch\u00f6tz","orcid":"https://orcid.org/0000-0003-1844-3865","observed_orcids":["https://orcid.org/0000-0003-1844-3865"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sch\u00f6tz, Matthias","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.86080002784729,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.86080002784729,"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":0.12610000371932983,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.0026000000070780516,"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/nilpotent-lie-algebras","display_name":"nilpotent Lie algebras","score":0.9679999947547913},{"id":"https://openalex.org/keywords/universal-enveloping-algebra","display_name":"universal enveloping algebra","score":0.9860000014305115},{"id":"https://openalex.org/keywords/irreducible-representations","display_name":"irreducible representations","score":0.8370000123977661},{"id":"https://openalex.org/keywords/unbounded-operators","display_name":"unbounded operators","score":0.6610000133514404},{"id":"https://openalex.org/keywords/semiprime-ideals","display_name":"semiprime ideals","score":0.8320000171661377},{"id":"https://openalex.org/keywords/primitive-ideals","display_name":"primitive ideals","score":0.8759999871253967},{"id":"https://openalex.org/keywords/operator-algebras","display_name":"operator algebras","score":0.8379999995231628},{"id":"https://openalex.org/keywords/real-algebraic-geometry","display_name":"real algebraic geometry","score":0.8399999737739563}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8083999752998352},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.5720999836921692},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5486000180244446},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.4684000015258789},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.45080000162124634},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.40230000019073486},{"id":"https://openalex.org/C185579658","wikidata":"https://www.wikidata.org/wiki/Q3554813","display_name":"Affine variety","level":3,"score":0.39719998836517334},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3709999918937683},{"id":"https://openalex.org/C2777103148","wikidata":"https://www.wikidata.org/wiki/Q445569","display_name":"Complexification","level":2,"score":0.3440000116825104},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.3434999883174896},{"id":"https://openalex.org/C45804927","wikidata":"https://www.wikidata.org/wiki/Q17098947","display_name":"Minimal ideal","level":4,"score":0.3361999988555908},{"id":"https://openalex.org/C155058155","wikidata":"https://www.wikidata.org/wiki/Q1673406","display_name":"Universal enveloping algebra","level":3,"score":0.3156000077724457},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.3046000003814697},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.2989000082015991},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.27869999408721924},{"id":"https://openalex.org/C56781331","wikidata":"https://www.wikidata.org/wiki/Q765289","display_name":"Semiprime","level":3,"score":0.26899999380111694},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.2687999904155731},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C145620117","wikidata":"https://www.wikidata.org/wiki/Q2989763","display_name":"Commutator","level":4,"score":0.25920000672340393},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.2542000114917755}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.28113","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28113","pdf_url":"https://arxiv.org/pdf/2610.28113","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.2610.28113","doi":"https://doi.org/10.48550/arxiv.2610.28113","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.28113","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:2610.28113","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28113","pdf_url":"https://arxiv.org/pdf/2610.28113","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223126207.pdf","grobid_xml":"https://content.openalex.org/works/W7223126207.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1527351491","https://openalex.org/W1967344706","https://openalex.org/W1999576403","https://openalex.org/W2070852332","https://openalex.org/W2077162779","https://openalex.org/W2077300652","https://openalex.org/W2085352155","https://openalex.org/W2155263740","https://openalex.org/W2162178369","https://openalex.org/W2321930835","https://openalex.org/W2952177788","https://openalex.org/W3201714619","https://openalex.org/W4254742099","https://openalex.org/W4405046022"],"related_works":["https://openalex.org/W4405046022","https://openalex.org/W2109228878","https://openalex.org/W164560920","https://openalex.org/W2006727684","https://openalex.org/W2001618379","https://openalex.org/W4394651107","https://openalex.org/W2280526863","https://openalex.org/W4213099163","https://openalex.org/W4289780927","https://openalex.org/W2118337499"],"abstract_inverted_index":{"We":[0],"prove":[1],"a":[2,12,47,66],"real":[3,15,24,119,129,141],"Nullstellensatz":[4,68,130],"for":[5,131],"the":[6,31,59,73,82,86,92,106,116,126],"universal":[7],"enveloping":[8],"algebra":[9,17,111],"U(g)":[10,22,40,62],"of":[11,21,33,35,39,61,75,103,108,118,121,140],"nilpotent":[13],"finite-dimensional":[14],"Lie":[16],"g:":[18],"An":[19],"ideal":[20,71],"is":[23,30,72,125],"if":[25,28],"and":[26],"only":[27,80],"it":[29],"intersection":[32,74],"kernels":[34],"irreducible":[36,135],"integrable":[37],"*-representations":[38,87],"by":[41],"(in":[42],"general":[43],"unbounded)":[44],"operators":[45],"on":[46,81,88],"Hilbert":[48,89],"space.":[49],"For":[50],"this,":[51],"we":[52],"build":[53],"upon":[54],"some":[55],"classical":[56],"results":[57,147],"about":[58,148],"complexification":[60],"that":[63],"lead":[64,145],"to":[65,97,146],"complex":[67],"(every":[69],"semiprime":[70],"primitive":[76],"ideals),":[77],"but":[78],"focus":[79],"``real":[83],"points'',":[84],"i.e.,":[85],"spaces.":[90],"On":[91],"technical":[93],"side,":[94],"this":[95],"requires":[96],"take":[98],"into":[99,115],"account":[100],"an":[101],"involution":[102],"U(g),":[104],"namely,":[105],"antipode":[107],"its":[109],"Hopf":[110],"structure,":[112],"which":[113],"goes":[114],"definition":[117],"ideals":[120],"U(g).":[122],"Our":[123],"result":[124],"first":[127],"noncommutative":[128],"*-algebras":[132,150],"with":[133],"unbounded":[134],"*-representations,":[136],"demonstrating":[137],"how":[138],"methods":[139,156],"algebraic":[142],"geometry":[143],"can":[144],"operator":[149],"also":[151],"in":[152],"situations":[153],"where":[154],"C*-algebraic":[155],"fail.":[157]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-22T00:00:00"}