{"title":"Hecke symmetries associated with twisted polynomial algebras in 3 indeterminates","authors":"Nikita Shishmarov, Serge Skryabin","doi":"10.1016/j.jalgebra.2024.11.012","DOIUrl":null,"url":null,"abstract":"<div><div>We consider Hecke symmetries on a 3-dimensional vector space with the associated <em>R</em>-symmetric algebra isomorphic to the polynomial algebra <span><math><mi>k</mi><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>]</mo></math></span> twisted by an automorphism. The main result states that any such a Hecke symmetry is itself a twist of a Hecke symmetry with the associated <em>R</em>-symmetric algebra isomorphic to <span><math><mi>k</mi><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>]</mo></math></span>. This allows us to describe equivalence classes of such Hecke symmetries.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"665 ","pages":"Pages 538-570"},"PeriodicalIF":0.8000,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869324006197","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We consider Hecke symmetries on a 3-dimensional vector space with the associated R-symmetric algebra isomorphic to the polynomial algebra twisted by an automorphism. The main result states that any such a Hecke symmetry is itself a twist of a Hecke symmetry with the associated R-symmetric algebra isomorphic to . This allows us to describe equivalence classes of such Hecke symmetries.
期刊介绍：
The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.
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