{"title":"Certain linear isomorphisms for hyperalgebras relative to a Chevalley group","authors":"Yutaka Yoshii","doi":"10.1142/s0219498825501853","DOIUrl":null,"url":null,"abstract":"<p>Let <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span> be a simply connected and simple algebraic group defined and split over a finite prime field <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>𝔽</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span><span></span> of <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>p</mi></math></span><span></span> elements. In this paper, using an <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>𝔽</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span><span></span>-linear map splitting Frobenius endomorphism on a hyperalgebra relative to <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span>, we obtain some <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>𝔽</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span><span></span>-linear isomorphisms induced by multiplication in the hyperalgebra.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"27 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra and Its Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219498825501853","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let be a simply connected and simple algebraic group defined and split over a finite prime field of elements. In this paper, using an -linear map splitting Frobenius endomorphism on a hyperalgebra relative to , we obtain some -linear isomorphisms induced by multiplication in the hyperalgebra.
期刊介绍：
The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.
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