{"id":"https://openalex.org/W7212072097","doi":"https://doi.org/10.48550/arxiv.2609.07377","title":"The Classification of the Rota-Baxter Operators on Four-dimensional Grassmann Algebra","display_name":"The Classification of the Rota-Baxter Operators on Four-dimensional Grassmann Algebra","publication_year":2026,"publication_date":"2026-09-07","ids":{"openalex":"https://openalex.org/W7212072097","doi":"https://doi.org/10.48550/arxiv.2609.07377"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.07377","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.07377","pdf_url":"https://arxiv.org/pdf/2609.07377","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/2609.07377","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005583044","display_name":"Kamran Shakoor","orcid":"https://orcid.org/0000-0002-9880-2815","observed_orcids":["https://orcid.org/0000-0002-9880-2815"]},"institutions":[{"id":"https://openalex.org/I43879129","display_name":"Government College University, Lahore","ror":"https://ror.org/040gec961","country_code":"PK","type":"education","lineage":["https://openalex.org/I43879129"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Shakoor, Kamran","raw_affiliation_strings":["Abdus Salam School of Mathematical Sciences , GC University , Lahore- Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Abdus Salam School of Mathematical Sciences , GC University , Lahore- Pakistan","institution_ids":["https://openalex.org/I43879129"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5150998218","display_name":"Noor-ul-Ain","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I43879129","display_name":"Government College University, Lahore","ror":"https://ror.org/040gec961","country_code":"PK","type":"education","lineage":["https://openalex.org/I43879129"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Noor-ul-Ain","raw_affiliation_strings":["Abdus Salam School of Mathematical Sciences , GC University , Lahore- Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Abdus Salam School of Mathematical Sciences , GC University , Lahore- Pakistan","institution_ids":["https://openalex.org/I43879129"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I43879129"],"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":0.9984999895095825,"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":0.9984999895095825,"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":9.999999747378752e-05,"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"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rota-baxter-operators","display_name":"Rota-Baxter operators","score":1.0},{"id":"https://openalex.org/keywords/exterior-algebra","display_name":"exterior algebra","score":0.9509999752044678},{"id":"https://openalex.org/keywords/operator-classification","display_name":"operator classification","score":0.6959999799728394}],"concepts":[{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.6740999817848206},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6693000197410583},{"id":"https://openalex.org/C94863793","wikidata":"https://www.wikidata.org/wiki/Q1196652","display_name":"Exterior algebra","level":3,"score":0.6287999749183655},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.565500020980835},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.4702000021934509},{"id":"https://openalex.org/C60321788","wikidata":"https://www.wikidata.org/wiki/Q1197190","display_name":"Multilinear algebra","level":5,"score":0.43050000071525574},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.3628000020980835},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35339999198913574},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.3352000117301941},{"id":"https://openalex.org/C26238338","wikidata":"https://www.wikidata.org/wiki/Q2377336","display_name":"Multivector","level":5,"score":0.3246999979019165},{"id":"https://openalex.org/C188971069","wikidata":"https://www.wikidata.org/wiki/Q1636734","display_name":"Universal algebra","level":3,"score":0.29409998655319214},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.27619999647140503},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2549999952316284},{"id":"https://openalex.org/C35958075","wikidata":"https://www.wikidata.org/wiki/Q1425077","display_name":"Spectral theorem","level":3,"score":0.25440001487731934}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.07377","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.07377","pdf_url":"https://arxiv.org/pdf/2609.07377","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.2609.07377","doi":"https://doi.org/10.48550/arxiv.2609.07377","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.07377","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:2609.07377","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.07377","pdf_url":"https://arxiv.org/pdf/2609.07377","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212072097.pdf","grobid_xml":"https://content.openalex.org/works/W7212072097.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1982291787","https://openalex.org/W7127656475","https://openalex.org/W4411336299","https://openalex.org/W2963304292","https://openalex.org/W2784496575","https://openalex.org/W4400023848","https://openalex.org/W4408056727","https://openalex.org/W2388047715","https://openalex.org/W2799254629","https://openalex.org/W7158624676"],"abstract_inverted_index":{"The":[0],"purpose":[1],"of":[2],"this":[3],"paper":[4],"is":[5],"to":[6],"classify":[7],"all":[8],"the":[9,20],"Rota-Baxter":[10],"operators":[11],"explicitly":[12],"on":[13],"Grassmann":[14],"algebra":[15],"in":[16],"dimension":[17],"four":[18],"over":[19],"reals.":[21]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-10T00:00:00"}
