{"id":"https://openalex.org/W7213605155","doi":"https://doi.org/10.48550/arxiv.2609.20363","title":"Range-compatible homomorphisms on Hermitian matrices","display_name":"Range-compatible homomorphisms on Hermitian matrices","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213605155","doi":"https://doi.org/10.48550/arxiv.2609.20363"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.20363","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20363","pdf_url":"https://arxiv.org/pdf/2609.20363","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/2609.20363","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016953630","display_name":"Cl\u00e9ment de Seguins Pazzis","orcid":"https://orcid.org/0000-0001-8777-4698","observed_orcids":["https://orcid.org/0000-0001-8777-4698"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Pazzis, Cl\u00e9ment de Seguins","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5016953630"],"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.8744999766349792,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.8744999766349792,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.07840000092983246,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.01860000006854534,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrices","score":0.9620000123977661},{"id":"https://openalex.org/keywords/group-homomorphisms","display_name":"group homomorphisms","score":0.7429999709129333},{"id":"https://openalex.org/keywords/skew-hermitian-matrices","display_name":"skew-Hermitian matrices","score":0.6970000267028809}],"concepts":[{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.8271999955177307},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8090000152587891},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.6525999903678894},{"id":"https://openalex.org/C31671303","wikidata":"https://www.wikidata.org/wiki/Q650741","display_name":"Division ring","level":3,"score":0.6309000253677368},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6129000186920166},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.567300021648407},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.5361999869346619},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43059998750686646},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4275999963283539},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4124000072479248},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.40230000019073486},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38749998807907104},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38109999895095825},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.2957000136375427},{"id":"https://openalex.org/C81901731","wikidata":"https://www.wikidata.org/wiki/Q331348","display_name":"Overdetermined system","level":2,"score":0.2872999906539917},{"id":"https://openalex.org/C62555958","wikidata":"https://www.wikidata.org/wiki/Q6042601","display_name":"Integer matrix","level":5,"score":0.28369998931884766},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2809999883174896},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.27399998903274536},{"id":"https://openalex.org/C56553554","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix ring","level":3,"score":0.2736000120639801},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.2662000060081482},{"id":"https://openalex.org/C2988629283","wikidata":"https://www.wikidata.org/wiki/Q44337","display_name":"Complex matrix","level":2,"score":0.2587999999523163},{"id":"https://openalex.org/C2781409172","wikidata":"https://www.wikidata.org/wiki/Q17056802","display_name":"Involution (esoterism)","level":3,"score":0.257099986076355},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.2563999891281128},{"id":"https://openalex.org/C149488123","wikidata":"https://www.wikidata.org/wiki/Q17098730","display_name":"Matrix analysis","level":3,"score":0.2538999915122986}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.20363","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20363","pdf_url":"https://arxiv.org/pdf/2609.20363","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.2609.20363","doi":"https://doi.org/10.48550/arxiv.2609.20363","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.20363","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:2609.20363","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20363","pdf_url":"https://arxiv.org/pdf/2609.20363","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/W7213605155.pdf","grobid_xml":"https://content.openalex.org/works/W7213605155.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2163082165","https://openalex.org/W7127569631","https://openalex.org/W7223470607","https://openalex.org/W2012659134","https://openalex.org/W2095705286","https://openalex.org/W2355673374","https://openalex.org/W2069193460","https://openalex.org/W2158388199","https://openalex.org/W2319049247","https://openalex.org/W2363804776"],"abstract_inverted_index":{"Let":[0],"$\\mathbb{D}$":[1],"be":[2,16,121],"a":[3,49,79,124],"division":[4],"ring":[5],"with":[6,29,42],"an":[7,17],"involution":[8],"$x":[9],"\\mapsto":[10],"x^\\star$,":[11],"and":[12,33,99,110,135],"$n":[13],"\\geq":[14],"2$":[15],"integer.":[18],"Denote":[19],"by":[20,34],"$\\mathcal{H}_n(\\mathbb{D})$":[21,61],"the":[22,36,53,72,97,100,105,114],"set":[23,37],"of":[24,38,83,129,132,139],"all":[25,39,57],"$n$-by-$n$":[26],"Hermitian":[27,130],"matrices":[28,40,131],"entries":[30],"in":[31,104,111,113,123],"$\\mathbb{D}$,":[32],"$\\mathcal{A}\\mathcal{H}_n(\\mathbb{D})$":[35,66],"$A-A^\\star$":[41],"$A":[43],"\\in":[44],"\\mathcal{M}_n(\\mathbb{D})$.":[45],"Here,":[46],"we":[47],"give":[48],"complete":[50],"solution":[51,87],"to":[52,62,67,78,88,107,120],"following":[54],"problem:":[55],"Determine":[56],"group":[58],"homomorphisms":[59],"from":[60,65],"$\\mathbb{D}^n$":[63,68],"(respectively,":[64],"unless":[69],"$(-)^\\star$":[70,95],"is":[71,96],"identity)":[73],"that":[74],"take":[75],"every":[76],"matrix":[77],"right":[80],"linear":[81],"combination":[82],"its":[84],"columns.":[85],"The":[86],"this":[89],"problem":[90],"was":[91],"already":[92],"known":[93],"when":[94],"identity,":[98],"novelty":[101],"here":[102],"lies":[103],"generalization":[106],"arbitrary":[108],"involutions,":[109],"particular":[112],"noncommutative":[115],"case.":[116],"These":[117],"results":[118],"are":[119],"used":[122],"subsequent":[125],"article":[126],"on":[127,136],"subspaces":[128],"bounded":[133],"rank,":[134],"large":[137],"spaces":[138],"diagonalisable":[140],"matrices.":[141]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-19T00:00:00"}