{"title":"斯泰恩德代数上的张量代数","authors":"H.E.A. Campbell, Paul Selick, Jie Wu","doi":"10.1016/j.jpaa.2024.107730","DOIUrl":null,"url":null,"abstract":"<div><p>It is known that unstable Steenrod module structure on the polynomial algebra <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>[</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>]</mo><mo>≅</mo><msup><mrow><mi>H</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><msup><mrow><mo>(</mo><mi>R</mi><msup><mrow><mi>P</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>)</mo></mrow><mrow><mi>N</mi></mrow></msup><mo>;</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> obtained by forgetting the multiplication is isomorphic to that arising from a twisted action of <span><math><msup><mrow><mi>Sq</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>. We show that the same theorem holds for tensor algebras. As in the abelian case, the result is applied to produce a decomposition of the tensor algebra into “weight spaces”.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Tensor algebras over the Steenrod algebra\",\"authors\":\"H.E.A. Campbell, Paul Selick, Jie Wu\",\"doi\":\"10.1016/j.jpaa.2024.107730\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>It is known that unstable Steenrod module structure on the polynomial algebra <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>[</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>]</mo><mo>≅</mo><msup><mrow><mi>H</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><msup><mrow><mo>(</mo><mi>R</mi><msup><mrow><mi>P</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>)</mo></mrow><mrow><mi>N</mi></mrow></msup><mo>;</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> obtained by forgetting the multiplication is isomorphic to that arising from a twisted action of <span><math><msup><mrow><mi>Sq</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>. We show that the same theorem holds for tensor algebras. As in the abelian case, the result is applied to produce a decomposition of the tensor algebra into “weight spaces”.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022404924001270\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022404924001270","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
It is known that unstable Steenrod module structure on the polynomial algebra obtained by forgetting the multiplication is isomorphic to that arising from a twisted action of . We show that the same theorem holds for tensor algebras. As in the abelian case, the result is applied to produce a decomposition of the tensor algebra into “weight spaces”.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
