{"id":"https://openalex.org/W4400368274","doi":"https://doi.org/10.1142/s0218196724500383","title":"Axial view on pseudo-composition algebras and train algebras of rank 3","display_name":"Axial view on pseudo-composition algebras and train algebras of rank 3","publication_year":2024,"publication_date":"2024-07-05","ids":{"openalex":"https://openalex.org/W4400368274","doi":"https://doi.org/10.1142/s0218196724500383"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196724500383","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0218196724500383","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020970040","display_name":"Ilya Gorshkov","orcid":"https://orcid.org/0000-0002-6239-2092"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]},{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Ilya Gorshkov","raw_affiliation_strings":["Saint Petersburg State University, Saint Petersburg, Russia","Sobolev Institute of Mathematics, Novosibirsk, Russia","Sobolev Institute of Mathematics, Novosibirsk, Russia; Saint Petersburg State University, Saint Petersburg, Russia;","Sobolev Institute of Mathematics, Novosibirsk, Russia;","Institute of Mathematics, Novosibirsk, Russia; Saint Petersburg State University, Saint Petersburg, Russia;"],"raw_orcid":"https://orcid.org/0000-0002-6239-2092","affiliations":[{"raw_affiliation_string":"Saint Petersburg State University, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I172901346"]},{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia","institution_ids":["https://openalex.org/I4210096862"]},{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia; Saint Petersburg State University, Saint Petersburg, Russia;","institution_ids":["https://openalex.org/I4210096862","https://openalex.org/I172901346"]},{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia;","institution_ids":["https://openalex.org/I4210096862"]},{"raw_affiliation_string":"Institute of Mathematics, Novosibirsk, Russia; Saint Petersburg State University, Saint Petersburg, Russia;","institution_ids":["https://openalex.org/I172901346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080411616","display_name":"A. S. Mamontov","orcid":"https://orcid.org/0000-0002-0324-5287"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]},{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Andrey Mamontov","raw_affiliation_strings":["Saint Petersburg State University, Saint Petersburg, Russia","Sobolev Institute of Mathematics, Novosibirsk, Russia","Sobolev Institute of Mathematics, Novosibirsk, Russia; Saint Petersburg State University, Saint Petersburg, Russia;","Sobolev Institute of Mathematics, Novosibirsk, Russia;"],"raw_orcid":"https://orcid.org/0000-0002-0324-5287","affiliations":[{"raw_affiliation_string":"Saint Petersburg State University, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I172901346"]},{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia","institution_ids":["https://openalex.org/I4210096862"]},{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia; Saint Petersburg State University, Saint Petersburg, Russia;","institution_ids":["https://openalex.org/I4210096862","https://openalex.org/I172901346"]},{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia;","institution_ids":["https://openalex.org/I4210096862"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067257345","display_name":"Alexey Staroletov","orcid":"https://orcid.org/0000-0002-3914-6758"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]},{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Alexey Staroletov","raw_affiliation_strings":["Sobolev Institute of Mathematics, Novosibirsk, Russia","Sobolev Institute of Mathematics, Novosibirsk, Russia;","Institute of Mathematics, Novosibirsk, Russia; Saint Petersburg State University, Saint Petersburg, Russia;","Sobolev Institute of Mathematics, Novosibirsk, Russia; Saint Petersburg State University, Saint Petersburg, Russia;"],"raw_orcid":"https://orcid.org/0000-0002-3914-6758","affiliations":[{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia","institution_ids":["https://openalex.org/I4210096862"]},{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia;","institution_ids":["https://openalex.org/I4210096862"]},{"raw_affiliation_string":"Institute of Mathematics, Novosibirsk, Russia; Saint Petersburg State University, Saint Petersburg, Russia;","institution_ids":["https://openalex.org/I172901346"]},{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia; Saint Petersburg State University, Saint Petersburg, Russia;","institution_ids":["https://openalex.org/I4210096862","https://openalex.org/I172901346"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5020970040"],"corresponding_institution_ids":["https://openalex.org/I172901346","https://openalex.org/I4210096862"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19921067,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":"06","first_page":"937","last_page":"960"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9988999962806702,"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":0.9988999962806702,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9959999918937683,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9868000149726868,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.91853928565979},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.8159272074699402},{"id":"https://openalex.org/keywords/composition","display_name":"Composition (language)","score":0.727918803691864},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4671458899974823},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4133714735507965},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2793181538581848},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.05193445086479187}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.91853928565979},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.8159272074699402},{"id":"https://openalex.org/C40231798","wikidata":"https://www.wikidata.org/wiki/Q1333743","display_name":"Composition (language)","level":2,"score":0.727918803691864},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4671458899974823},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4133714735507965},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2793181538581848},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.05193445086479187},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196724500383","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0218196724500383","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W656351880","https://openalex.org/W1727118510","https://openalex.org/W1980866547","https://openalex.org/W2019228890","https://openalex.org/W2068669536","https://openalex.org/W2073427371","https://openalex.org/W2080789539","https://openalex.org/W2081102812","https://openalex.org/W2087903393","https://openalex.org/W2095365956","https://openalex.org/W2467726098","https://openalex.org/W2529190546","https://openalex.org/W2886365342"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"pseudo-composition":[3],"algebras":[4,7,18,37],"and":[5,66],"train":[6],"of":[8,27,32,51,69],"rank":[9],"3":[10],"generated":[11],"by":[12],"idempotents":[13,28],"are":[14,38],"characterized":[15],"as":[16],"axial":[17,36],"with":[19],"fusion":[20],"laws":[21],"derived":[22],"from":[23],"the":[24,52,64],"Peirce":[25],"decompositions":[26],"in":[29],"these":[30],"classes":[31],"algebras.":[33,71],"The":[34],"corresponding":[35],"called":[39],"[Formula:":[40,45],"see":[41,46],"text]-axial":[42],"algebras,":[43],"where":[44],"text]":[47],"is":[48],"an":[49],"element":[50],"ground":[53],"field.":[54],"As":[55],"a":[56],"first":[57],"step":[58],"toward":[59],"their":[60],"classification,":[61],"we":[62],"describe":[63],"2-":[65],"3-generated":[67],"subalgebras":[68],"such":[70]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}