{"id":"https://openalex.org/W7214620632","doi":"https://doi.org/10.48550/arxiv.2609.31417","title":"A Proof of the Second brick-Brauer-Thrall Conjecture for $E$-infinite algebras","display_name":"A Proof of the Second brick-Brauer-Thrall Conjecture for $E$-infinite algebras","publication_year":2026,"publication_date":"2026-09-25","ids":{"openalex":"https://openalex.org/W7214620632","doi":"https://doi.org/10.48550/arxiv.2609.31417"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.31417","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31417","pdf_url":"https://arxiv.org/pdf/2609.31417","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/2609.31417","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010441207","display_name":"Kaveh Mousavand","orcid":"https://orcid.org/0000-0003-0651-1138","observed_orcids":["https://orcid.org/0000-0003-0651-1138"]},"institutions":[{"id":"https://openalex.org/I142637625","display_name":"Okinawa Institute of Science and Technology Graduate University","ror":"https://ror.org/02qg15b79","country_code":"JP","type":"education","lineage":["https://openalex.org/I142637625"]},{"id":"https://openalex.org/I51768193","display_name":"Royal Military College of Canada","ror":"https://ror.org/04yr71909","country_code":"CA","type":"education","lineage":["https://openalex.org/I51768193"]}],"countries":["CA","JP"],"is_corresponding":false,"raw_author_name":"Mousavand, Kaveh","raw_affiliation_strings":["Department of Mathematics and Computer Science , Royal Military College of Canada , Kingston ON , Canada","Unit of Representation Theory and Algebraic Combinatorics , Okinawa Institute of Science and Technology , Okinawa , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science , Royal Military College of Canada , Kingston ON , Canada","institution_ids":["https://openalex.org/I51768193"]},{"raw_affiliation_string":"Unit of Representation Theory and Algebraic Combinatorics , Okinawa Institute of Science and Technology , Okinawa , Japan","institution_ids":["https://openalex.org/I142637625"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021195529","display_name":"Charles Paquette","orcid":"https://orcid.org/0000-0002-2901-1921","observed_orcids":["https://orcid.org/0000-0002-2901-1921"]},"institutions":[{"id":"https://openalex.org/I142637625","display_name":"Okinawa Institute of Science and Technology Graduate University","ror":"https://ror.org/02qg15b79","country_code":"JP","type":"education","lineage":["https://openalex.org/I142637625"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Paquette, Charles","raw_affiliation_strings":["Unit of Representation Theory and Algebraic Combinatorics , Okinawa Institute of Science and Technology , Okinawa , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Unit of Representation Theory and Algebraic Combinatorics , Okinawa Institute of Science and Technology , Okinawa , Japan","institution_ids":["https://openalex.org/I142637625"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9990000128746033,"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":0.9990000128746033,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.0003000000142492354,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/tau-tilting-theory","display_name":"\u03c4-tilting theory","score":0.824999988079071},{"id":"https://openalex.org/keywords/finite-dimensional-algebras","display_name":"finite-dimensional algebras","score":0.6930000185966492},{"id":"https://openalex.org/keywords/dense-orbits","display_name":"dense orbits","score":0.34299999475479126}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8226000070571899},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8118000030517578},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.611299991607666},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.5268999934196472},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.5098000168800354},{"id":"https://openalex.org/C203701370","wikidata":"https://www.wikidata.org/wiki/Q1047547","display_name":"Algebraically closed field","level":2,"score":0.47929999232292175},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4478999972343445},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.42980000376701355},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42260000109672546},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.41760000586509705},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.39739999175071716},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39320001006126404},{"id":"https://openalex.org/C128814272","wikidata":"https://www.wikidata.org/wiki/Q837314","display_name":"Collatz conjecture","level":3,"score":0.3619999885559082},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.2572999894618988},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.31417","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31417","pdf_url":"https://arxiv.org/pdf/2609.31417","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.2609.31417","doi":"https://doi.org/10.48550/arxiv.2609.31417","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.31417","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:2609.31417","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31417","pdf_url":"https://arxiv.org/pdf/2609.31417","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":[{"id":"https://openalex.org/G8487176158","display_name":"The 2nd brick-Brauer-Thrall conjecture via tau-tilting theory and representation varieties","funder_award_id":"24K16908","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320315625","display_name":"Canadian Defence Academy","ror":"https://ror.org/01h02mz80"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214620632.pdf","grobid_xml":"https://content.openalex.org/works/W7214620632.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W4386475483","https://openalex.org/W4389115365","https://openalex.org/W4407764959","https://openalex.org/W4414458443","https://openalex.org/W7151301789","https://openalex.org/W7166198606"],"related_works":["https://openalex.org/W7166198606","https://openalex.org/W4386044062","https://openalex.org/W4304172792","https://openalex.org/W3137477909","https://openalex.org/W4394644487","https://openalex.org/W7111377620","https://openalex.org/W4408537717","https://openalex.org/W3101896149","https://openalex.org/W4414458443","https://openalex.org/W4413948065"],"abstract_inverted_index":{"For":[0,136],"any":[1,68],"finite-dimensional":[2],"algebra":[3],"$A$":[4,14,43,72,109,119],"over":[5],"an":[6,45,103],"algebraically":[7],"closed":[8],"field,":[9],"we":[10,27,77,106,123],"prove":[11,124],"that":[12,29,82,108,125],"if":[13,30,115,118],"is":[15,32,110,120],"$E$-infinite,":[16],"then":[17,42],"the":[18,37,131,159],"Second":[19,133],"brick-Brauer-Thrall":[20,134],"Conjecture":[21,129],"holds":[22],"for":[23,54,97],"$A$.":[24],"In":[25],"fact,":[26],"show":[28,63],"there":[31],"a":[33,79,98],"rational":[34],"ray":[35],"outside":[36],"$\u03c4$-tilting":[38],"fan":[39],"of":[40,48,51,71,161],"$A$,":[41],"admits":[44],"infinite":[46],"family":[47],"$\u03b8$-stable":[49,95],"bricks":[50],"dimension":[52],"$d$,":[53],"some":[55,162],"positive":[56],"integer":[57],"$d$":[58],"and":[59,88,116,150],"weight":[60,100],"$\u03b8$.":[61,101],"To":[62],"our":[64,139,147],"main":[65],"result,":[66],"from":[67],"$\u03c4$-regular":[69],"component":[70,81],"with":[73,146],"no":[74,85],"dense":[75,86],"orbit,":[76],"obtain":[78],"brick":[80],"also":[83],"has":[84],"orbit":[87],"whose":[89],"points":[90],"in":[91,158],"general":[92],"position":[93],"are":[94],"modules":[96],"given":[99],"As":[102],"important":[104,156],"consequence,":[105],"conclude":[107],"stably-discrete":[111],"(also":[112],"called":[113],"multiplicity-free)":[114],"only":[117],"$E$-finite.":[121],"Moreover,":[122],"Demonet's":[126],"(lattice":[127],"point)":[128],"implies":[130],"stable":[132],"Conjecture.":[135],"$E$-infinite":[137],"algebras,":[138],"results":[140],"settle":[141],"several":[142],"open":[143,164],"conjectures.":[144],"Together":[145],"earlier":[148],"work":[149],"recent":[151],"developments,":[152],"this":[153],"leads":[154],"to":[155],"reductions":[157],"study":[160],"challenging":[163],"problems.":[165]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-29T00:00:00"}
