{"id":"https://openalex.org/W7220448292","doi":"https://doi.org/10.48550/arxiv.2610.02463","title":"Graded twisted reflection matrices of GL-type","display_name":"Graded twisted reflection matrices of GL-type","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7220448292","doi":"https://doi.org/10.48550/arxiv.2610.02463"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02463","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02463","pdf_url":"https://arxiv.org/pdf/2610.02463","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/2610.02463","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091921009","display_name":"D. Algethami","orcid":"https://orcid.org/0009-0003-5204-8241","observed_orcids":["https://orcid.org/0009-0003-5204-8241"]},"institutions":[{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Algethami, D.","raw_affiliation_strings":["Moscow Institute of Physics and Technology ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Moscow Institute of Physics and Technology ,","institution_ids":["https://openalex.org/I153845743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059667733","display_name":"Andrey Mudrov","orcid":"https://orcid.org/0000-0003-0651-1357","observed_orcids":["https://orcid.org/0000-0003-0651-1357"]},"institutions":[{"id":"https://openalex.org/I4210136004","display_name":"University of Bisha","ror":"https://ror.org/040548g92","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210136004"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Mudrov, A.","raw_affiliation_strings":["Department of Mathematics , College of Science , University of Bisha , P.O. Box 551 , Bisha 61922 , Saudi Arabia,","Institutskiy per. , Dolgoprudny , Moscow Region , 141701 , Russia,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , College of Science , University of Bisha , P.O. Box 551 , Bisha 61922 , Saudi Arabia,","institution_ids":["https://openalex.org/I4210136004"]},{"raw_affiliation_string":"Institutskiy per. , Dolgoprudny , Moscow Region , 141701 , Russia,","institution_ids":[]}]}],"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":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":0.5893999934196472,"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":0.5893999934196472,"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":0.36959999799728394,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.013799999840557575,"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/locality-principle","display_name":"locality principle","score":0.7419999837875366},{"id":"https://openalex.org/keywords/lie-superalgebras","display_name":"Lie superalgebras","score":0.8899999856948853},{"id":"https://openalex.org/keywords/classification-of-solutions","display_name":"classification of solutions","score":0.45399999618530273}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.718500018119812},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.7149999737739563},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.6340000033378601},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5060999989509583},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45010000467300415},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.41670000553131104},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.38609999418258667},{"id":"https://openalex.org/C78804095","wikidata":"https://www.wikidata.org/wiki/Q1133024","display_name":"Lie superalgebra","level":5,"score":0.3765999972820282},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.35249999165534973},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.30469998717308044},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.2793000042438507},{"id":"https://openalex.org/C2779808786","wikidata":"https://www.wikidata.org/wiki/Q6664603","display_name":"Locality","level":2,"score":0.2718999981880188},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.260699987411499},{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.2515000104904175},{"id":"https://openalex.org/C2778778035","wikidata":"https://www.wikidata.org/wiki/Q967960","display_name":"Mathematics Subject Classification","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.02463","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02463","pdf_url":"https://arxiv.org/pdf/2610.02463","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.2610.02463","doi":"https://doi.org/10.48550/arxiv.2610.02463","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02463","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:2610.02463","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02463","pdf_url":"https://arxiv.org/pdf/2610.02463","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/G1973846972","display_name":null,"funder_award_id":"00115","funder_id":"https://openalex.org/F4320324099","funder_display_name":"Russian Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320319621","display_name":"University of Bisha","ror":"https://ror.org/040548g92"},{"id":"https://openalex.org/F4320324099","display_name":"Russian Science Foundation","ror":"https://ror.org/03y2gwe85"},{"id":"https://openalex.org/F4320330091","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220448292.pdf","grobid_xml":"https://content.openalex.org/works/W7220448292.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7151265762"],"related_works":["https://openalex.org/W4391450117","https://openalex.org/W3121682557","https://openalex.org/W87788410","https://openalex.org/W6966728415","https://openalex.org/W3003510388","https://openalex.org/W2265101806","https://openalex.org/W3098810629","https://openalex.org/W2064701026","https://openalex.org/W1964554159","https://openalex.org/W7098251141"],"abstract_inverted_index":{"We":[0,42],"classify":[1],"constant":[2],"numerical":[3],"solutions":[4,48,61],"of":[5,39,67,74],"the":[6,12,44,55,64],"$\\Z_2$-graded":[7],"twisted":[8],"reflection":[9,40],"equation":[10],"for":[11,36,54],"fundamental":[13],"$GL$-type":[14],"R-matrix":[15],"and":[16,46,49],"an":[17,88],"arbitrary":[18],"parity":[19],"sequence,":[20],"without":[21],"assuming":[22],"evenness":[23],"or":[24],"invertibility.":[25],"The":[26,71],"classification":[27,66],"is":[28,80,87],"based":[29],"on":[30],"a":[31,75,81],"four-index":[32],"locality":[33],"principle":[34],"established":[35],"this":[37],"type":[38],"equation.":[41],"determine":[43],"singular":[45],"invertible":[47,60],"recover":[50],"previously":[51],"conjectured":[52],"matrices":[53],"minimal":[56],"symmetric":[57],"grading.":[58],"Even":[59],"comply":[62],"with":[63],"recent":[65],"graded":[68],"Satake":[69],"diagrams.":[70],"classical":[72],"stabilizer":[73],"full-support":[76],"lower-triangular":[77],"non-even":[78],"family":[79],"Lie":[82,90],"superalgebra":[83],"whose":[84],"even":[85],"part":[86],"electrical":[89],"algebra.":[91]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-06T00:00:00"}