{"id":"https://openalex.org/W7223035595","doi":"https://doi.org/10.48550/arxiv.2610.24568","title":"Commutative exact superalgebras and super-modular tensor categories","display_name":"Commutative exact superalgebras and super-modular tensor categories","publication_year":2026,"publication_date":"2026-10-17","ids":{"openalex":"https://openalex.org/W7223035595","doi":"https://doi.org/10.48550/arxiv.2610.24568"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.24568","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.24568","pdf_url":"https://arxiv.org/pdf/2610.24568","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/2610.24568","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038812456","display_name":"Alexander Zuevsky","orcid":"https://orcid.org/0000-0002-2792-8883","observed_orcids":["https://orcid.org/0000-0002-2792-8883"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zuevsky, A.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5038812456"],"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9976000189781189,"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":0.9976000189781189,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.000699999975040555,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.00019999999494757503,"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/superalgebras","display_name":"superalgebras","score":0.9070000052452087},{"id":"https://openalex.org/keywords/vertex-operator-algebras","display_name":"vertex operator algebras","score":0.7979999780654907},{"id":"https://openalex.org/keywords/ribbon-categories","display_name":"ribbon categories","score":0.7990000247955322},{"id":"https://openalex.org/keywords/fermion-condensation","display_name":"fermion condensation","score":0.6200000047683716},{"id":"https://openalex.org/keywords/toric-code","display_name":"toric code","score":0.9340000152587891},{"id":"https://openalex.org/keywords/free-fermions","display_name":"free fermions","score":0.9459999799728394}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8339999914169312},{"id":"https://openalex.org/C186863843","wikidata":"https://www.wikidata.org/wiki/Q3977654","display_name":"Superalgebra","level":3,"score":0.7228999733924866},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6207000017166138},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.5552999973297119},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5174999833106995},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.49729999899864197},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.46650001406669617},{"id":"https://openalex.org/C75174853","wikidata":"https://www.wikidata.org/wiki/Q190629","display_name":"Centralizer and normalizer","level":2,"score":0.44339999556541443},{"id":"https://openalex.org/C2780392137","wikidata":"https://www.wikidata.org/wiki/Q17121801","display_name":"Ribbon","level":2,"score":0.4025999903678894},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39430001378059387},{"id":"https://openalex.org/C197273675","wikidata":"https://www.wikidata.org/wiki/Q13220368","display_name":"Representation theory","level":2,"score":0.38839998841285706},{"id":"https://openalex.org/C162205778","wikidata":"https://www.wikidata.org/wiki/Q4915506","display_name":"Biproduct","level":4,"score":0.3862999975681305},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.37619999051094055},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.3653999865055084},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.33309999108314514},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.3264000117778778},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.32199999690055847},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.31189998984336853},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3041999936103821},{"id":"https://openalex.org/C153491289","wikidata":"https://www.wikidata.org/wiki/Q3912012","display_name":"Category of groups","level":4,"score":0.30390000343322754},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.30169999599456787},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28949999809265137},{"id":"https://openalex.org/C31937215","wikidata":"https://www.wikidata.org/wiki/Q956233","display_name":"Simple module","level":3,"score":0.267300009727478},{"id":"https://openalex.org/C46263353","wikidata":"https://www.wikidata.org/wiki/Q4596935","display_name":"2-category","level":4,"score":0.26600000262260437},{"id":"https://openalex.org/C54884031","wikidata":"https://www.wikidata.org/wiki/Q217413","display_name":"Category theory","level":2,"score":0.265500009059906},{"id":"https://openalex.org/C109593458","wikidata":"https://www.wikidata.org/wiki/Q5262626","display_name":"Derived category","level":3,"score":0.25369998812675476},{"id":"https://openalex.org/C186921422","wikidata":"https://www.wikidata.org/wiki/Q318737","display_name":"Abelian category","level":3,"score":0.250900000333786}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.24568","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.24568","pdf_url":"https://arxiv.org/pdf/2610.24568","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.2610.24568","doi":"https://doi.org/10.48550/arxiv.2610.24568","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.24568","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.24568","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.24568","pdf_url":"https://arxiv.org/pdf/2610.24568","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/G1741043573","display_name":null,"funder_award_id":"67985840","funder_id":"https://openalex.org/F4320322482","funder_display_name":"Akademie V\u011bd \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G3967893287","display_name":null,"funder_award_id":"RVO67985840","funder_id":"https://openalex.org/F4320322482","funder_display_name":"Akademie V\u011bd \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320322482","display_name":"Akademie V\u011bd \u010cesk\u00e9 Republiky","ror":"https://ror.org/053avzc18"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223035595.pdf","grobid_xml":"https://content.openalex.org/works/W7223035595.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W1498940994","https://openalex.org/W4394664355","https://openalex.org/W4406781137","https://openalex.org/W7163887158"],"related_works":["https://openalex.org/W4402387444","https://openalex.org/W2616334666","https://openalex.org/W7147387484","https://openalex.org/W2998606553","https://openalex.org/W3154642787","https://openalex.org/W7215810850","https://openalex.org/W7203929055","https://openalex.org/W4400269449","https://openalex.org/W2998053623","https://openalex.org/W1790464069"],"abstract_inverted_index":{"We":[0,160],"extend":[1],"the":[2,31,38,43,47,59,72,84,88,98,101,115,133,168,172],"theory":[3],"of":[4,19,33,46,49,83,100,117,135],"commutative":[5,63],"exact":[6,111],"algebras":[7],"in":[8,56,66,138,145],"braided":[9,25,122],"finite":[10,123],"tensor":[11,124],"categories":[12],"(Shimizu-Yadav)":[13],"to":[14],"superalgebras,":[15],"motivated":[16],"by":[17,97,143],"extensions":[18],"vertex":[20],"operator":[21],"(super)algebras.":[22],"For":[23,104],"a":[24,62,121,136,139],"category":[26,32,45,116,125,141],"$\\C$":[27,57,105,149],"let":[28],"$\\B=\\C^{\\gr}$":[29],"be":[30],"$\\mathbb":[34],"Z/2$-graded":[35],"objects":[36],"with":[37,87,177],"Koszul-signed":[39],"braiding.":[40],"It":[41,131],"is":[42,58,95,120,129,132,150,154,158],"underlying":[44],"supercategory":[48],"Creutzig-Kanade-McRae.":[50],"A":[51],"supercommutative":[52],"superalgebra":[53],"$A=A_0\\oplus":[54],"A_1$":[55],"same":[60],"as":[61],"algebra":[64],"$\\bA$":[65,108,153],"$\\B$,":[67],"and":[68,78,107,110,152,171,175,179],"super-local":[69,118],"modules":[70,119],"are":[71,81],"local":[73],"$\\bA$-modules.":[74],"Hence":[75],"rigidity,":[76],"pivotality":[77],"ribbon":[79,89,151],"statements":[80],"instances":[82],"ordinary":[85],"theorems,":[86],"condition":[90],"$\u03b8_{A_0}=\\id$,":[91],"$\u03b8_{A_1}=\\varepsilon\\,\\id$,":[92],"where":[93],"$\\varepsilon=\\pm1$":[94],"fixed":[96],"statistics":[99],"odd":[102],"part.":[103],"non-degenerate":[106,140],"haploid":[109],"we":[112],"prove":[113],"that":[114],"whose":[126],"M\u00fcger":[127],"center":[128],"$\\mathsf{sVect}$.":[130],"centralizer":[134],"fermion":[137,170],"obtained":[142],"condensing":[144],"$\\C\\boxtimes(\\text{toric":[146],"code})$.":[147],"If":[148],"symmetric":[155],"Frobenius":[156],"it":[157],"ribbon.":[159],"construct":[161],"examples":[162],"from":[163],"graded":[164],"simple":[165],"currents,":[166],"treat":[167],"free":[169],"symplectic":[173],"fermion,":[174],"compare":[176],"Creutzig-Kanade-McRae":[178],"Creutzig-McRae-Shimizu-Yadav.":[180]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-21T00:00:00"}
