{"id":"https://openalex.org/W7204997098","doi":"https://doi.org/10.20944/preprints202609.0078.v1","title":"Idempotent-Free Non-Solvable Evolution Algebras over C","display_name":"Idempotent-Free Non-Solvable Evolution Algebras over C","publication_year":2026,"publication_date":"2026-09-01","ids":{"openalex":"https://openalex.org/W7204997098","doi":"https://doi.org/10.20944/preprints202609.0078.v1"},"language":"en","primary_location":{"id":"doi:10.20944/preprints202609.0078.v1","doi":"https://doi.org/10.20944/preprints202609.0078.v1","is_oa":true,"landing_page_url":"https://doi.org/10.20944/preprints202609.0078.v1","pdf_url":null,"source":{"id":"https://openalex.org/S6309402219","display_name":"Preprints.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"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":"posted-content"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.20944/preprints202609.0078.v1","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147896412","display_name":"Xing-Yu Hu","orcid":"https://orcid.org/0009-0004-4351-413X","observed_orcids":["https://orcid.org/0009-0004-4351-413X","https://orcid.org/0009-0007-9953-9362"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xing-Yu Hu","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0004-4351-413X","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5149047320","display_name":"Ran Wen","orcid":"https://orcid.org/0009-0009-2478-4480","observed_orcids":["https://orcid.org/0009-0009-2478-4480"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ran Wen","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":2,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9994999766349792,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9994999766349792,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.0,"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/evolution-algebras","display_name":"evolution algebras","score":0.9959999918937683},{"id":"https://openalex.org/keywords/idempotents","display_name":"idempotents","score":0.9200000166893005},{"id":"https://openalex.org/keywords/solvable-algebras","display_name":"solvable algebras","score":0.871999979019165},{"id":"https://openalex.org/keywords/derived-series","display_name":"derived series","score":0.8029999732971191},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.6710000038146973}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.8504999876022339},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8126999735832214},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6708999872207642},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.647599995136261},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.6337000131607056},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.5752000212669373},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.44839999079704285},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44519999623298645},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4268999993801117},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.41339999437332153},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4074999988079071},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.38659998774528503},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.35440000891685486},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.35440000891685486},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35429999232292175},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.31150001287460327},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.30660000443458557},{"id":"https://openalex.org/C100856211","wikidata":"https://www.wikidata.org/wiki/Q674689","display_name":"Clifford algebra","level":3,"score":0.298799991607666},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2904999852180481},{"id":"https://openalex.org/C21696900","wikidata":"https://www.wikidata.org/wiki/Q1333055","display_name":"Semiring","level":2,"score":0.25369998812675476}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.20944/preprints202609.0078.v1","doi":"https://doi.org/10.20944/preprints202609.0078.v1","is_oa":true,"landing_page_url":"https://doi.org/10.20944/preprints202609.0078.v1","pdf_url":null,"source":{"id":"https://openalex.org/S6309402219","display_name":"Preprints.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"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":"posted-content"},{"id":"pmh:oai:arXiv.org:2609.25023","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25023","pdf_url":"https://arxiv.org/pdf/2609.25023","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.2609.25023","doi":"https://doi.org/10.48550/arxiv.2609.25023","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.25023","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":"doi:10.20944/preprints202609.0078.v1","doi":"https://doi.org/10.20944/preprints202609.0078.v1","is_oa":true,"landing_page_url":"https://doi.org/10.20944/preprints202609.0078.v1","pdf_url":null,"source":{"id":"https://openalex.org/S6309402219","display_name":"Preprints.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"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":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204997098.pdf","grobid_xml":"https://content.openalex.org/works/W7204997098.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4415025991"],"related_works":["https://openalex.org/W7214084374","https://openalex.org/W7222355305","https://openalex.org/W7223454620","https://openalex.org/W4417448526","https://openalex.org/W4380876065","https://openalex.org/W2124058942","https://openalex.org/W2510601185","https://openalex.org/W4220937841","https://openalex.org/W2795311341","https://openalex.org/W2100951308"],"abstract_inverted_index":{"A":[0],"recent":[1],"conjecture":[2,43],"states":[3],"that":[4],"a":[5,23,76,99],"finite-dimensional":[6],"complex":[7,38,114],"evolution":[8,39,83,138],"algebra":[9,59],"is":[10,44,60,71,106,136],"solvable":[11],"if":[12,15],"and":[13,49,70],"only":[14,104],"it":[16],"has":[17,53],"no":[18],"non-zero":[19,100],"idempotents.":[20],"We":[21,122],"exhibit":[22],"three-dimensional":[24,37],"counterexample":[25,52],"over":[26,62],"C":[27],"whose":[28,85,103],"isomorphism":[29],"class":[30],"already":[31],"appears":[32],"in":[33,46,116],"the":[34,42,54,72,91,94,125,129,133],"classification":[35],"of":[36,65,75,79,132],"algebras.":[40],"Since":[41],"known":[45],"dimensions":[47],"one":[48],"two,":[50],"this":[51],"smallest":[55],"possible":[56],"dimension.":[57],"The":[58],"defined":[61],"every":[63,117],"field":[64],"characteristic":[66],"different":[67],"from":[68],"2":[69],"exceptional":[73,92],"member":[74],"one-parameter":[77],"family":[78],"pairwise":[80],"non-isomorphic":[81],"non-solvable":[82],"algebras":[84,112],"idempotents":[86],"are":[87],"determined":[88],"explicitly.":[89],"For":[90],"parameter,":[93],"derived":[95,134],"series":[96,135],"stabilises":[97],"at":[98,119],"two-dimensional":[101],"subalgebra":[102],"idempotent":[105],"zero.":[107],"Direct":[108],"sums":[109],"with":[110],"zero":[111],"give":[113],"counterexamples":[115],"dimension":[118],"least":[120],"three.":[121],"also":[123],"prove":[124],"conjectured":[126],"equivalence":[127],"whenever":[128],"stable":[130],"term":[131],"an":[137],"algebra.":[139]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-09-02T00:00:00"}