Duality theory of $p$-adic Hopf algebras
We show the monoidal functoriality of Schikhof duality, and cultivate new duality theory of $p$-adic Hopf algebras. Through the duality, we introduce two sorts of $p$-adic Pontryagin dualities. One is a duality between discrete Abelian groups and affine formal group schemes of specific type, and the...
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| Format: | Article |
| Language: | English |
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Shahid Beheshti University
2021-01-01
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| Series: | Categories and General Algebraic Structures with Applications |
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| Online Access: | https://cgasa.sbu.ac.ir/article_87523_90bb198d291c498c8cd128ce4c24faad.pdf |
| _version_ | 1818557915996356608 |
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| author | Tomoki Mihara |
| author_facet | Tomoki Mihara |
| author_sort | Tomoki Mihara |
| collection | DOAJ |
| description | We show the monoidal functoriality of Schikhof duality, and cultivate new duality theory of $p$-adic Hopf algebras. Through the duality, we introduce two sorts of $p$-adic Pontryagin dualities. One is a duality between discrete Abelian groups and affine formal group schemes of specific type, and the other one is a duality between profinite Abelian groups and analytic groups of specific type. We extend Amice transform to a $p$-adic Fourier transform compatible with the second $p$-adic Pontryagin duality. As applications, we give explicit presentations of a universal family of irreducible $p$-adic unitary Banach representations of the open unit disc of the general linear group and its $q$-deformation in the case of dimension $2$. |
| first_indexed | 2024-12-14T00:05:57Z |
| format | Article |
| id | doaj.art-8468c47b0e7442cc8a22abb28f2003b3 |
| institution | Directory Open Access Journal |
| issn | 2345-5853 2345-5861 |
| language | English |
| last_indexed | 2024-12-14T00:05:57Z |
| publishDate | 2021-01-01 |
| publisher | Shahid Beheshti University |
| record_format | Article |
| series | Categories and General Algebraic Structures with Applications |
| spelling | doaj.art-8468c47b0e7442cc8a22abb28f2003b32022-12-21T23:26:02ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612021-01-011418111810.29252/cgasa.14.1.8187523Duality theory of $p$-adic Hopf algebrasTomoki Mihara0University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571 JapanWe show the monoidal functoriality of Schikhof duality, and cultivate new duality theory of $p$-adic Hopf algebras. Through the duality, we introduce two sorts of $p$-adic Pontryagin dualities. One is a duality between discrete Abelian groups and affine formal group schemes of specific type, and the other one is a duality between profinite Abelian groups and analytic groups of specific type. We extend Amice transform to a $p$-adic Fourier transform compatible with the second $p$-adic Pontryagin duality. As applications, we give explicit presentations of a universal family of irreducible $p$-adic unitary Banach representations of the open unit disc of the general linear group and its $q$-deformation in the case of dimension $2$.https://cgasa.sbu.ac.ir/article_87523_90bb198d291c498c8cd128ce4c24faad.pdfpontryagin duality$p$-adichopf |
| spellingShingle | Tomoki Mihara Duality theory of $p$-adic Hopf algebras Categories and General Algebraic Structures with Applications pontryagin duality $p$-adic hopf |
| title | Duality theory of $p$-adic Hopf algebras |
| title_full | Duality theory of $p$-adic Hopf algebras |
| title_fullStr | Duality theory of $p$-adic Hopf algebras |
| title_full_unstemmed | Duality theory of $p$-adic Hopf algebras |
| title_short | Duality theory of $p$-adic Hopf algebras |
| title_sort | duality theory of p adic hopf algebras |
| topic | pontryagin duality $p$-adic hopf |
| url | https://cgasa.sbu.ac.ir/article_87523_90bb198d291c498c8cd128ce4c24faad.pdf |
| work_keys_str_mv | AT tomokimihara dualitytheoryofpadichopfalgebras |