{"id":"https://openalex.org/W4385096547","doi":"https://doi.org/10.3842/sigma.2026.099","title":"Twisted Post-Groups and Skew Trusses","display_name":"Twisted Post-Groups and Skew Trusses","publication_year":2026,"publication_date":"2026-10-19","ids":{"openalex":"https://openalex.org/W4385096547","doi":"https://doi.org/10.3842/sigma.2026.099"},"language":"en","primary_location":{"id":"doi:10.3842/sigma.2026.099","doi":"https://doi.org/10.3842/sigma.2026.099","is_oa":true,"landing_page_url":"https://doi.org/10.3842/sigma.2026.099","pdf_url":"https://sigma-journal.com/2026/099/sigma26-099.pdf","source":{"id":"https://openalex.org/S190431191","display_name":"Symmetry Integrability and Geometry Methods and Applications","issn_l":"1815-0659","issn":["1815-0659"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-c","jufo-1","norway-1","oarl","poland-70","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310321802","host_organization_name":"National Academy of Sciences of Ukraine","host_organization_lineage":["https://openalex.org/P4310321802"],"host_organization_lineage_names":["National Academy of Sciences of Ukraine"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry, Integrability and Geometry: Methods and Applications","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sigma-journal.com/2026/099/sigma26-099.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101010688","display_name":"Shukun Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I184681353","display_name":"Anhui University of Science and Technology","ror":"https://ror.org/00q9atg80","country_code":"CN","type":"education","lineage":["https://openalex.org/I184681353"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shukun Wang","raw_affiliation_strings":["Anhui University of Science and Technology, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Anhui University of Science and Technology, P.R. China","institution_ids":["https://openalex.org/I184681353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101010688"],"corresponding_institution_ids":["https://openalex.org/I184681353"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.00743078,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"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":0.0008999999845400453,"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/T12504","display_name":"Mathematics and Applications","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/skew-braces","display_name":"skew braces","score":0.6819999814033508},{"id":"https://openalex.org/keywords/hopf-algebras","display_name":"Hopf algebras","score":0.7730000019073486},{"id":"https://openalex.org/keywords/rings","display_name":"rings","score":0.3330000042915344}],"concepts":[{"id":"https://openalex.org/C29712632","wikidata":"https://www.wikidata.org/wiki/Q1627597","display_name":"Hopf algebra","level":3,"score":0.7627605199813843},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6962165832519531},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5589672923088074},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5294496417045593},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.5122224688529968},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.44450637698173523},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.438308984041214},{"id":"https://openalex.org/C76572486","wikidata":"https://www.wikidata.org/wiki/Q2602722","display_name":"Group ring","level":3,"score":0.43129318952560425},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.42084038257598877},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3322429060935974},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32796335220336914},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10491952300071716},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3842/sigma.2026.099","doi":"https://doi.org/10.3842/sigma.2026.099","is_oa":true,"landing_page_url":"https://doi.org/10.3842/sigma.2026.099","pdf_url":"https://sigma-journal.com/2026/099/sigma26-099.pdf","source":{"id":"https://openalex.org/S190431191","display_name":"Symmetry Integrability and Geometry Methods and Applications","issn_l":"1815-0659","issn":["1815-0659"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-c","jufo-1","norway-1","oarl","poland-70","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310321802","host_organization_name":"National Academy of Sciences of Ukraine","host_organization_lineage":["https://openalex.org/P4310321802"],"host_organization_lineage_names":["National Academy of Sciences of Ukraine"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry, Integrability and Geometry: Methods and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2307.10535","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2307.10535","pdf_url":"https://arxiv.org/pdf/2307.10535","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.2307.10535","doi":"https://doi.org/10.48550/arxiv.2307.10535","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2307.10535","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":"doi:10.3842/sigma.2026.099","doi":"https://doi.org/10.3842/sigma.2026.099","is_oa":true,"landing_page_url":"https://doi.org/10.3842/sigma.2026.099","pdf_url":"https://sigma-journal.com/2026/099/sigma26-099.pdf","source":{"id":"https://openalex.org/S190431191","display_name":"Symmetry Integrability and Geometry Methods and Applications","issn_l":"1815-0659","issn":["1815-0659"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-c","jufo-1","norway-1","oarl","poland-70","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310321802","host_organization_name":"National Academy of Sciences of Ukraine","host_organization_lineage":["https://openalex.org/P4310321802"],"host_organization_lineage_names":["National Academy of Sciences of Ukraine"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry, Integrability and Geometry: Methods and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323708","display_name":"Anhui University of Science and Technology","ror":"https://ror.org/00q9atg80"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385096547.pdf","grobid_xml":"https://content.openalex.org/works/W4385096547.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1503971394","https://openalex.org/W1633336122","https://openalex.org/W1985885288","https://openalex.org/W2011906442","https://openalex.org/W2040571085","https://openalex.org/W2051979364","https://openalex.org/W2080819269","https://openalex.org/W2209202465","https://openalex.org/W2302011925","https://openalex.org/W2339197221","https://openalex.org/W2761641915","https://openalex.org/W2922214840","https://openalex.org/W2962844998","https://openalex.org/W2963945370","https://openalex.org/W4221162317","https://openalex.org/W4322505912","https://openalex.org/W4360985402","https://openalex.org/W4387652097","https://openalex.org/W4387984926","https://openalex.org/W4389708577","https://openalex.org/W4409466176","https://openalex.org/W7162096457"],"related_works":["https://openalex.org/W4409466176","https://openalex.org/W4380993211","https://openalex.org/W2055745562","https://openalex.org/W7077064735","https://openalex.org/W7139160577","https://openalex.org/W4407425483","https://openalex.org/W1991665494","https://openalex.org/W2087078124","https://openalex.org/W4407310128","https://openalex.org/W4403964485"],"abstract_inverted_index":{"To":[0],"understand":[1],"the":[2,14,20,50,60,69,81,128,136,157],"origin":[3],"of":[4,16,22,32,53,62,71,83,130,138],"post-groups":[5,65,133],"introduced":[6],"by":[7],"Bai,":[8],"Guo,":[9],"Sheng,":[10],"and":[11,41,74,108,134],"Tang":[12],"from":[13],"perspective":[15],"rings,":[17],"we":[18,27,57,126],"introduce":[19,104],"notion":[21,137],"(weak)":[23,131,139],"twisted":[24,34,44,64,78,94,105,117,122,132,140,147],"post-groups.":[25],"First,":[26],"show":[28,144],"that":[29,42,59,75,90,114,145],"every":[30,76,91,146],"element":[31],"a":[33,38,43,84,99,116,121],"post-group":[35,45,79,95],"belongs":[36],"to":[37,68,98,152],"unique":[39],"group,":[40],"can":[46],"be":[47],"viewed":[48],"as":[49],"disjoint":[51],"union":[52],"such":[54],"groups.":[55],"Next,":[56],"prove":[58],"category":[61,70],"weak":[63],"is":[66],"isomorphic":[67],"skew":[72,86],"trusses,":[73],"two-sided":[77,85,93],"admits":[80],"structure":[82],"brace.":[87],"It":[88],"follows":[89],"abelian":[92],"gives":[96,150],"rise":[97,151],"radical":[100],"ring.":[101],"We":[102,143],"then":[103],"post-Lie":[106,118,123],"algebras":[107],"investigate":[109],"their":[110],"algebraic":[111],"properties,":[112],"showing":[113],"differentiating":[115],"group":[119],"yields":[120],"algebra.":[124,160],"Finally,":[125],"consider":[127],"linearization":[129],"propose":[135],"post-Hopf":[141,148],"algebras.":[142],"algebra":[149],"another":[153],"Hopf":[154,159],"algebra,":[155],"called":[156],"sub-adjacent":[158]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2023-07-23T00:00:00"}