{"id":"https://openalex.org/W7225347752","doi":"https://doi.org/10.5281/zenodo.23983573","title":"The Non-Abelian M\u00f6bius Klein Transformation: Sectors as Irreducible Representations and Fusion as Selection","display_name":"The Non-Abelian M\u00f6bius Klein Transformation: Sectors as Irreducible Representations and Fusion as Selection","publication_year":2026,"publication_date":"2026-11-05","ids":{"openalex":"https://openalex.org/W7225347752","doi":"https://doi.org/10.5281/zenodo.23983573"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23983573","doi":"https://doi.org/10.5281/zenodo.23983573","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23983573","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23983573","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5143630282","display_name":"L\u00e1szl\u00f3 M\u00e1rk","orcid":"https://orcid.org/0009-0006-5033-633X","observed_orcids":["https://orcid.org/0009-0006-5033-633X"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mark, Laszlo","raw_affiliation_strings":["Independent Researcher"],"raw_orcid":"https://orcid.org/0009-0006-5033-633X","affiliations":[{"raw_affiliation_string":"Independent Researcher","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5143630282"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":5,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.5253999829292297,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.5253999829292297,"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/T10849","display_name":"Finite Group Theory Research","score":0.20430000126361847,"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"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.15449999272823334,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/non-orientable-surfaces","display_name":"non-orientable surfaces","score":0.7039999961853027},{"id":"https://openalex.org/keywords/branched-coverings","display_name":"branched coverings","score":0.7519999742507935},{"id":"https://openalex.org/keywords/graph-covers","display_name":"graph covering","score":0.6119999885559082},{"id":"https://openalex.org/keywords/irreducible-representations","display_name":"irreducible representations","score":0.6990000009536743},{"id":"https://openalex.org/keywords/fusion-rules","display_name":"fusion rules","score":0.8090000152587891},{"id":"https://openalex.org/keywords/isotypic-components","display_name":"isotypic components","score":0.8980000019073486},{"id":"https://openalex.org/keywords/selection-rules","display_name":"selection rules","score":0.6309999823570251},{"id":"https://openalex.org/keywords/fano-plane","display_name":"Fano plane","score":0.925000011920929},{"id":"https://openalex.org/keywords/trefoil-knot","display_name":"trefoil knot","score":0.7979999780654907},{"id":"https://openalex.org/keywords/figure-eight-knot","display_name":"figure-eight knot","score":0.9950000047683716},{"id":"https://openalex.org/keywords/holonomy","display_name":"holonomy","score":0.6639999747276306},{"id":"https://openalex.org/keywords/spherical-harmonics","display_name":"spherical harmonics","score":0.753000020980835},{"id":"https://openalex.org/keywords/spinors","display_name":"spinors","score":0.6589999794960022}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7003999948501587},{"id":"https://openalex.org/C72409365","wikidata":"https://www.wikidata.org/wiki/Q558339","display_name":"Dihedral group","level":3,"score":0.5241000056266785},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4361000061035156},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4341999888420105},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.3873000144958496},{"id":"https://openalex.org/C142292226","wikidata":"https://www.wikidata.org/wiki/Q13690522","display_name":"Irreducible representation","level":2,"score":0.37290000915527344},{"id":"https://openalex.org/C162329640","wikidata":"https://www.wikidata.org/wiki/Q332648","display_name":"Covering space","level":2,"score":0.37070000171661377},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3668000102043152},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.36390000581741333},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.34769999980926514},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.32839998602867126},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.3091000020503998},{"id":"https://openalex.org/C169611556","wikidata":"https://www.wikidata.org/wiki/Q230689","display_name":"Contractible space","level":2,"score":0.3059000074863434},{"id":"https://openalex.org/C82927061","wikidata":"https://www.wikidata.org/wiki/Q178192","display_name":"Cross product","level":2,"score":0.3050999939441681},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C92957085","wikidata":"https://www.wikidata.org/wiki/Q1412905","display_name":"Permutation group","level":3,"score":0.289000004529953},{"id":"https://openalex.org/C95635736","wikidata":"https://www.wikidata.org/wiki/Q1786640","display_name":"Wreath product","level":3,"score":0.2856999933719635},{"id":"https://openalex.org/C2779710842","wikidata":"https://www.wikidata.org/wiki/Q6086323","display_name":"Isospectral","level":2,"score":0.2842000126838684},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.2759000062942505},{"id":"https://openalex.org/C159876591","wikidata":"https://www.wikidata.org/wiki/Q662830","display_name":"Fundamental group","level":2,"score":0.27250000834465027},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C143782950","wikidata":"https://www.wikidata.org/wiki/Q40460","display_name":"Orbifold","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.26010000705718994}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23983573","doi":"https://doi.org/10.5281/zenodo.23983573","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23983573","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23983574","doi":"https://doi.org/10.5281/zenodo.23983574","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23983574","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23983573","doi":"https://doi.org/10.5281/zenodo.23983573","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23983573","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W7171110224","https://openalex.org/W7171133033","https://openalex.org/W7172387593","https://openalex.org/W7201956211","https://openalex.org/W7202126680","https://openalex.org/W7222888657","https://openalex.org/W7223477300","https://openalex.org/W7225344855"],"related_works":["https://openalex.org/W7225345602","https://openalex.org/W7225344855","https://openalex.org/W3217560774","https://openalex.org/W2750517262","https://openalex.org/W2171185722","https://openalex.org/W2326198964","https://openalex.org/W1556706487","https://openalex.org/W4310524616","https://openalex.org/W974931214","https://openalex.org/W7225340415"],"abstract_inverted_index":{"The":[0,134],"M\u00f6bius":[1],"Klein":[2],"Transformation":[3],"(MKT)":[4],"sorts":[5],"the":[6,13,32,54,88,93,97,104,110,114,116,120,124,128,131,147,172,176,180,186,196,199,218,221,226,231,234,243,260,264,282,290],"fields":[7,140],"on":[8,61,65,268],"a":[9,37,40,43,47,80,85,154,183,189,192,202,205,209,212,250,286],"non-orientable":[10,251],"space":[11],"by":[12,156],"deck":[14,55],"group":[15,22,56,106,215],"of":[16,25,31,49,90,96,107,137,175,188,198,220,230,257,281],"its":[17,246],"orientable":[18],"double":[19],"cover.":[20],"That":[21],"is":[23,35,39,46,75,84,179],"cyclic":[24],"order":[26,258],"2,":[27],"and":[28,42,64,71,87,118,123,130,150,171,233,245,263,284],"every":[29,269],"rule":[30,45,95],"MKT":[33],"canon":[34],"abelian:":[36],"sector":[38,74,139,169,190],"character,":[41],"selection":[44],"product":[48,89,145],"signs.":[50],"This":[51],"article":[52],"lets":[53],"be":[57],"any":[58],"finite":[59],"group,":[60],"free":[62],"covers":[63,66,102,166,229],"branched":[67],"along":[68],"points,":[69],"knots":[70],"graphs.":[72],"A":[73],"then":[76],"an":[77],"isotypic":[78],"component,":[79],"field":[81,288],"in":[82],"it":[83],"multiplet,":[86],"signs":[91],"becomes":[92],"fusion":[94],"irreducible":[98],"representations.":[99],"On":[100,249],"graph":[101],"with":[103,167,211,254],"symmetric":[105],"3":[108,138],"letters":[109],"spectrum":[111],"splits":[112],"into":[113,242],"trivial,":[115],"sign":[117],"twice":[119],"standard":[121,132],"sector,":[122],"3-sheeted":[125],"cover":[126,135],"keeps":[127],"trivial":[129,148],"one.":[133],"sum":[136],"vanishes":[141],"whenever":[142],"their":[143],"tensor":[144,270],"misses":[146],"representation,":[149],"generically":[151],"only":[152,279,285],"then;":[153],"bookkeeping":[155],"determinant":[157],"characters":[158,280],"gets":[159],"this":[160],"wrong.":[161],"Sunada's":[162],"isospectral":[163],"pairs":[164],"are":[165,217],"equal":[168],"content,":[170],"incidence":[173],"matrix":[174],"Fano":[177],"plane":[178],"transplantation.":[181],"Over":[182],"smooth":[184],"base":[185,244],"exponents":[187],"at":[191],"branch":[193],"edge":[194],"follow":[195],"eigenvalues":[197],"meridian,":[200],"so":[201],"reflection":[203],"gives":[204],"square-root":[206],"exponent.":[207],"At":[208],"vertex":[210],"polyhedral":[213],"local":[214],"they":[216],"degrees":[219],"spherical":[222],"harmonics":[223],"that":[224],"contain":[225],"representation.":[227],"Dihedral":[228],"trefoil":[232],"figure-eight":[235],"knot,":[236],"built":[237],"from":[238],"Fox":[239],"colourings,":[240],"split":[241],"2-dimensional":[247],"sectors.":[248],"flat":[252],"4-manifold":[253],"dihedral":[255],"holonomy":[256,265],"8":[259],"orientation":[261],"character":[262],"act":[266],"together":[267],"slice.":[271],"Around":[272],"2":[273],"quaternion":[274],"defects":[275],"frame":[276],"vectors":[277],"see":[278],"base,":[283],"spinor":[287],"sees":[289],"non-abelian":[291],"sector.":[292]},"counts_by_year":[{"year":2026,"cited_by_count":5}],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-06T00:00:00"}
