{"id":"https://openalex.org/W7213610768","doi":"https://doi.org/10.48550/arxiv.2609.20488","title":"Polynomial identities, central polynomials and cocharacters of $M_2(F)$ with $G$-graded involution","display_name":"Polynomial identities, central polynomials and cocharacters of $M_2(F)$ with $G$-graded involution","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213610768","doi":"https://doi.org/10.48550/arxiv.2609.20488"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.20488","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20488","pdf_url":"https://arxiv.org/pdf/2609.20488","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/2609.20488","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054897797","display_name":"Rafael Bezerra dos Santos","orcid":"https://orcid.org/0000-0002-9056-5624","observed_orcids":["https://orcid.org/0000-0002-9056-5624"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Santos, Rafael Bezerra dos","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136767410","display_name":"Lucas Reis","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Reis, Lucas","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":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/T11673","display_name":"Advanced Topics in Algebra","score":0.7544000148773193,"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":0.7544000148773193,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.20980000495910645,"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/T10849","display_name":"Finite Group Theory Research","score":0.0031999999191612005,"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/polynomial-identities","display_name":"polynomial identities","score":0.9869999885559082},{"id":"https://openalex.org/keywords/central-polynomials","display_name":"central polynomials","score":0.9810000061988831},{"id":"https://openalex.org/keywords/cocharacters","display_name":"cocharacters","score":0.8700000047683716},{"id":"https://openalex.org/keywords/matrix-algebra","display_name":"matrix algebra","score":0.640999972820282},{"id":"https://openalex.org/keywords/22-matrices","display_name":"2x2 matrices","score":0.7300000190734863},{"id":"https://openalex.org/keywords/finite-abelian-groups","display_name":"finite abelian groups","score":0.8130000233650208},{"id":"https://openalex.org/keywords/t-ideals","display_name":"T-ideals","score":0.8159999847412109},{"id":"https://openalex.org/keywords/t-spaces","display_name":"T-spaces","score":0.7089999914169312},{"id":"https://openalex.org/keywords/codimension","display_name":"codimension","score":0.875},{"id":"https://openalex.org/keywords/klein-group","display_name":"Klein group","score":0.6039999723434448},{"id":"https://openalex.org/keywords/pi-algebras","display_name":"PI-algebras","score":0.6859999895095825}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.819100022315979},{"id":"https://openalex.org/C2781409172","wikidata":"https://www.wikidata.org/wiki/Q17056802","display_name":"Involution (esoterism)","level":3,"score":0.7267000079154968},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5939000248908997},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.489300012588501},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4722999930381775},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39959999918937683},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.3537999987602234},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3472000062465668},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3312000036239624},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3246999979019165},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.29190000891685486},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.25600001215934753},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.2542000114917755}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.20488","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20488","pdf_url":"https://arxiv.org/pdf/2609.20488","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.2609.20488","doi":"https://doi.org/10.48550/arxiv.2609.20488","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.20488","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":"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":"pmh:oai:arXiv.org:2609.20488","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20488","pdf_url":"https://arxiv.org/pdf/2609.20488","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/G4373714938","display_name":null,"funder_award_id":"00133-21","funder_id":"https://openalex.org/F4320322980","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Minas Gerais"},{"id":"https://openalex.org/G4471733295","display_name":"REDE MINEIRA DE MATEM\u00c1TICA (RMMAT-MG)","funder_award_id":"RED-00133-21","funder_id":"https://openalex.org/F4320322980","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Minas Gerais"},{"id":"https://openalex.org/G4955648311","display_name":null,"funder_award_id":"RED-00133-21","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G5814379729","display_name":null,"funder_award_id":"420721/2025-8","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G6153887890","display_name":null,"funder_award_id":"RED-00133-21","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G8479983001","display_name":null,"funder_award_id":"420721/2025-8","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320322980","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Minas Gerais","ror":"https://ror.org/00nc55f03"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213610768.pdf","grobid_xml":"https://content.openalex.org/works/W7213610768.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7163034866"],"related_works":["https://openalex.org/W7213583182","https://openalex.org/W4388571202","https://openalex.org/W2324773814","https://openalex.org/W7163034866","https://openalex.org/W2011610228","https://openalex.org/W2119881977","https://openalex.org/W2076818315","https://openalex.org/W3030617018","https://openalex.org/W1966871989","https://openalex.org/W7120334352"],"abstract_inverted_index":{"Let":[0],"$F$":[1],"be":[2,9,16],"a":[3,10],"field":[4],"of":[5,19,39,42,45,48,51,67,73],"characteristic":[6],"zero,":[7],"$G$":[8],"finite":[11],"abelian":[12],"group":[13],"and":[14,35,44,60,83],"$M_2(F)$":[15,34],"the":[17,37,40,46,57,61,68,71,76,79],"algebra":[18],"$2\\times":[20],"2$":[21],"matrices":[22],"over":[23],"$F$.":[24],"In":[25],"this":[26],"paper,":[27],"we":[28,54],"consider":[29],"all":[30],"$G$-graded":[31],"involutions":[32],"on":[33],"determine":[36],"generators":[38],"$T_{(G,*)}$-ideal":[41],"identities":[43],"$T_{(G,*)}$-space":[47],"central":[49,85],"polynomials":[50],"$M_2(F)$.":[52],"Moreover,":[53],"explicitly":[55,90],"compute":[56],"$\\langle":[58],"n\\rangle$-cocharacter":[59],"$n$-th":[62],"$(G,":[63,80,86],"*)$-codimensions":[64,87],"for":[65],"most":[66],"gradings.":[69],"For":[70],"case":[72],"gradings":[74],"by":[75],"Klein":[77],"group,":[78],"*)$-central":[81],"codimensions":[82],"proper":[84],"are":[88],"also":[89],"computed.":[91]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-19T00:00:00"}