{"title":"A4与SO(3)模2上同调中的Steenrod闭参数理想","authors":"Henrik Rüping , Marc Stephan , Ergün Yalçın","doi":"10.1016/j.jpaa.2025.107899","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we classify the parameter ideals in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>B</mi><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>;</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> and in the Dickson algebra <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>B</mi><mi>SO</mi><mo>(</mo><mn>3</mn><mo>)</mo><mo>;</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> that are closed under Steenrod operations. Consequently, we obtain restrictions on the dimensions <span><math><mi>n</mi><mo>,</mo><mi>m</mi></math></span> for which <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> (and <span><math><mi>SO</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></span>) can act freely on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107899"},"PeriodicalIF":0.7000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Steenrod closed parameter ideals in the mod-2 cohomology of A4 and SO(3)\",\"authors\":\"Henrik Rüping , Marc Stephan , Ergün Yalçın\",\"doi\":\"10.1016/j.jpaa.2025.107899\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we classify the parameter ideals in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>B</mi><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>;</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> and in the Dickson algebra <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>B</mi><mi>SO</mi><mo>(</mo><mn>3</mn><mo>)</mo><mo>;</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> that are closed under Steenrod operations. Consequently, we obtain restrictions on the dimensions <span><math><mi>n</mi><mo>,</mo><mi>m</mi></math></span> for which <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> (and <span><math><mi>SO</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></span>) can act freely on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>.</div></div>\",\"PeriodicalId\":54770,\"journal\":{\"name\":\"Journal of Pure and Applied Algebra\",\"volume\":\"229 2\",\"pages\":\"Article 107899\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Pure and Applied Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022404925000386\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pure and Applied Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022404925000386","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Steenrod closed parameter ideals in the mod-2 cohomology of A4 and SO(3)
In this paper, we classify the parameter ideals in and in the Dickson algebra that are closed under Steenrod operations. Consequently, we obtain restrictions on the dimensions for which (and ) can act freely on .
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The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.
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